determine whether the sample may be biased. explain. a famous author of mystery novels wants to survey readers of her previous novels to get their opinion on possible new plot lines for future books. the author contacts six national book clubs and asks them to send out the survey to a random sample of the people who ordered her previous books through them.
Answers
The sample can be unrepresentative of all possible readers of the author's works as it mainly consists of people who have previously ordered her novels through particular book clubs.
what is sample size?The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.
First off, the sample solely consists of people who have already purchased her novels from the chosen book clubs. As a result, the sample does not include readers who purchase her books via independent bookstores or internet merchants, for example. Compared to those who ordered through the book clubs, these readers could have different thoughts on the new storylines.
Second, there may be selection bias because the sample is only made up of people who have read the author's works in the past. O
As a result, the sample can be unrepresentative of all possible readers of the author's works as it mainly consists of people who have previously ordered her novels through particular book clubs.
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Related Questions
I HAVE AN URGENT QUESTIONS!!!!
Answers
Thus, the area of the rectangular playground is found as 1500 sq. ft.
Explain about the area of rectangle:A parallelogram with four opposing, parallel, congruent sides is referred to as a rectangle. The rectangle's corners are at a right angle. The fact that a rectangle's sides are not all equal is the only distinction between it and a square.
A two-dimensional shape's area is the interior blank space. The quantity of space that a shape occupies is another way to define area. When calculating a rectangle's area, we multiply the length by the width of a rectangle.
Given that-
Perimeter P = 160 feetLength l = 50 feetLet the width = w feet.P = 2(l + w)
160 = 2 (50 + w)
80 = 50 +w
w = 80 - 50
w = 30 feet
area = length* width
area = 50*30
area = 1500 sq. ft
Thus, the area of the rectangular playground is found as 1500 sq. ft.
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Correct question-
The perimeter of the playground shown is 160 feet. Find the area.
Length is 50 ft.
1 The geometric mean of two positive integers a and b is 27 Find all possible
values of a and b
Answers
Answer:
(a, b) ∈ {(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}
Step-by-step explanation:
\(\sqrt{a\cdot b}=27\\\\(\sqrt{a\cdot b})^2=27^2\\\\a\cdot b=729\\\\\\729=27\cdot27=9\cdot81=3\cdot243=1\cdot729\)
So:
(a, b)∈{(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}
which of the following is not a measure of the degree of spread or dispersion of scores? a) mode b) standard deviation c) range d) variance
Answers
Answer: A. mode
Step-by-step explanation: Mode is not a measure of the degree of spread or dispersion of scores.
It takes Austin 8 hours longer than Elliott to construct a wooden chair in shop class. When the classmates work together, they can complete one chair in 3 hours. This situation can be represented by this expression, where t is the amount of time, in hours, it takes Elliott to complete a chair on his own.
Answers
The equivalent expression obtained using the least common multiple concept is \( \frac{6t + 24}{t^{2} +8}\)
To solve, we need to obtain the L. C. M of the denominator values :
The L. C. M of t and t + 8 = \( t^{2} + 8t\)
Hence,
\(\frac{3}{t} + \frac{3}{t+8} = \frac{6t + 24}{t^{2} +8}\)
Therefore, the equivalent expression which represents the situation described above ls ;\( \frac{6t + 24}{t^{2} + 8t}\)
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Answer:
D
Step-by-step explanation:
What is 20x8 divided by 3-5
Answers
Answer:
-80
Step-by-step explanation:
→ Complete the multiplication
20 × 8 = 160
→ Complete the take away
3 - 5 = -2
→ Divide the two answers from each other
160 ÷ -2 = -80
what is the median of the distribution
Answers
Answer:
The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.
Step-by-step explanation:
no
What is 35 to the nearest degree
Answers
I'm sorry, 35 is not a measure of angle and therefore cannot be rounded to the nearest degree. Are you asking for the sine, cosine, or tangent of 35 degrees?
Find the value of X express each answer as a decimal rounded to the nearest tenth.
Answers
Answer:
x = 15.6
Step-by-step explanation:
use the pythagorean theorem:
a² + b² = c²
a = 9
b = x
c = 18
(9)² + x² = (18)²
81 + x² = 324 subtract 81 from both sides
x² = 243 take the square root of both sides
x = √243
x = 15.6
THE THRID FUNDAMENTAL FORM A) What is the third fundamentalform of a differentiable surface and what is its geometricinterpretation? Proof B) What are its properties? Proof C) What is its relation to
Answers
A) The third fundamental form of a differentiable surface is a mathematical concept that characterizes the intrinsic geometry of the surface. It is defined in terms of the second derivatives of the surface's parameterization. Geometrically, the third fundamental form measures the rate of change of the surface's unit normal vector as one moves in the direction of the surface.
Proof:
The third fundamental form, denoted as III, is given by the equation:
III = -N · (d²r/du²) · (d²r/dv²) / |dr/du × dr/dv|,
where N is the unit normal vector to the surface, r(u, v) is the parameterization of the surface, and d²r/du² and d²r/dv² are the second derivatives of r with respect to u and v, respectively. |dr/du × dr/dv| represents the magnitude of the cross product of the partial derivatives of r.
B) The properties of the third fundamental form include:
1. Invariance under reparameterization: The third fundamental form is invariant under changes in the parameterization of the surface. This property ensures that the geometric information encoded by the third fundamental form remains consistent regardless of how the surface is parameterized.
2. Symmetry: The third fundamental form is symmetric with respect to the two variables u and v. In other words, swapping the roles of u and v does not change the value of the third fundamental form.
3. Relationship with the second fundamental form: The third fundamental form is related to the second fundamental form, which characterizes the extrinsic curvature of the surface. More specifically, the third fundamental form is expressed in terms of the second fundamental form as:
III = -N · L,
where L is the linear operator defined as:
L = (d²r/dv²) · S · (d²r/du²) - (d²r/dv²) · S · (d²r/dv²),
and S is the shape operator associated with the surface.
The proofs for these properties involve calculations using the definition and properties of the second fundamental form, as well as manipulation of the differential operators. These proofs require a more detailed understanding of differential geometry and are beyond the scope of this brief explanation.
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The distribution of random variable r has mean 10 and standard deviation 4. The distribution of random variable s has mean 7 and standard deviation 3. If r and s are independent, what are the mean and standard deviation of the distribution of r−s ?.
Answers
If \(X,Y\) are independent, we have the properties for expectation and variance,
\(\Bbb E[aX + bY] = a\,\Bbb E[X] + b\,\Bbb E[Y]\)
\(\Bbb V[aX + bY] = a^2\,\Bbb V[X] + b^2\,\Bbb V[Y]\)
where \(a,b\in\Bbb R\) are fixed.
Then
\(\Bbb E[R - S] = \Bbb E[R] - \Bbb E[S] = 10 - 7 = \boxed{3}\)
and
\(\Bbb V[R - S] = \Bbb V[R] + (-1)^2\, \Bbb V[S] = 4^2 + 3^2 = \boxed{5}\,{}^2 = 25\)
(recall that standard deviation = √(variance))
A-180
B-360
C-270
D-90
PLS HELP ASAP!!
Answers
Answer:
its d
Step-by-step explanation:
is (n x (n +1)) / 2 the same as (n/2)(n+1)
Answers
Answer:
nope
Step-by-step explanation:
simplify the first equation
Answer:
yes
Step-by-step explanation:
The associative and commutative properties of multiplication allow you to rearrange the product to the form shown in the question.
Division by 2 is effectively multiplication by 1/2.
\((n\times(n+1))/2\qquad\text{given}\\\\=\dfrac{n(n+1)}{2}=\dfrac{n}{2}(n+1)\\\\=\boxed{(n/2)(n+1)}\)
__
Additional comment
Evaluation of the expressions according to the order of operations will proceed differently for the two expressions.
For the first expression, evaluation steps are ...
add 1 to nmultiply the sum by ndivide the product by 2For the second expression, evaluation steps are ...
divide n by 2add 1 to nmultiply the results of these two operationsAs we said above, the properties of multiplication ensure the results are the same either way.
As a practical matter, for integer values of n, one of n and (n+1) will be even. It is usually convenient to divide the even number by 2. This means the evaluation might be ...
((n+1)/2)n . . . . for odd n(n+1)(n/2) . . . . for even nFor certain computer representations of the numbers, results may differ depending on the specific numbers and the order of evaluation.
13 m height
10 m
Find the exact volume of the cylinder.
-))
A)
6570 m3
B)
13071 m3
C)
260 m3
D)
32571 m3
Answers
Answer:
C) 260 m3
Step-by-step explanation:
1/3 x + y = 4 solve for y
Answers
hope this helps :)
The simplified answer to the equation is \(y=-\frac{1}{3}x+4\)
First, subtract \(\frac{1}{3}x\) on both sides.
\(y=-\frac{1}{3}x+4\)
You have isolated \(y\) by itself, and the equation can't be simplified further, so \(y=-\frac{1}{3}x+4\) is your answer.
An art student uses a roll of wallpaper to decorate two gift boxes. The student will use 3 1 3 yards of paper for one box and 5 6 yard of paper for the other box. The paper must be cut into pieces that are 1 6 yard long. How many pieces will the student cut to use for the gift boxes?
Answers
Answer:
25 pieces
Step-by-step explanation:
Given
\(Box_1 = 3\frac{1}{3}\)
\(Box_2 = \frac{5}{6}\)
\(Pieces = \frac{1}{6}\) yard
Required
Determine the number of pieces
First, we need to determine the total yards of paper
\(Total = Box_1 + Box_2\)
\(Total = 3\frac{1}{3} + \frac{5}{6}\)
\(Total = \frac{10}{3} + \frac{5}{6}\)
\(Total = \frac{20 + 5}{6}\)
\(Total = \frac{25}{6}\)
Divide by the size of the pieces to get the number of pieces
\(Number = Total/Pieces\)
\(Number = \frac{25}{6} / \frac{1}{6}\)
\(Number = \frac{25}{6} * \frac{6}{1}\)
\(Number = \frac{25}{1} * \frac{1}{1}\)
\(Number = 25\)
find the measure of the arc mDE=
Answers
Answer:
90°
Step-by-step explanation:
Hope it helps!!
The measure of Arc is 90 degree.
What is Arc?An "arc" is a smooth curve that connects two points in mathematics. In general, an arc is a section of a circle. It is essentially a portion of a circle's circumference.
A circle's arc is defined as a portion or segment of its circumference. A chord of a circle is a straight line that can be created by connecting the two ends of an arc. A semicircular arc is one whose length is exactly half that of a circle.
Since, m(arc EF) = Angle subtended by the arc EF at the center
= 146°
m(arc DE) = 90°
Thus, the measure of arc DE is 90 degree.
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A student has a gift box that measures 5in by 10in by 10in. The student knows that large items will have to be placed diagonally inside the box. What is the longest item that the student can wrap if the item is positioned
Answers
The longest item that the student can wrap if the item is positioned diagonally is 15 inches.
Assuming the length, breadth and height of the gift box be 10, 10 and 5 inches respectively. Thus, the diagonal on the base will be calculated using Pythagoras theorem.
Diagonal = ✓(10² + 10²)
Diagonal = ✓200
Diagonal = 14.14 inches
Now, the height is 5 inches and diagonal base is 14.14 inches. Thus, the diagonal equal to longest item will be -
Longest item = ✓(5² + 14.14²)
Longest item = ✓(25 + 200)
Longest item = ✓225
Longest item = 15 inch
Hence, 15 inch item can be positioned diagonally.
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The complete question is -
A student has a gift box that measures 5in by 10in by 10in. The student knows that large items will have to be placed diagonally inside the box. What is the longest item that the student can wrap if the item is positioned diagonally.
The integral expression ∫xcos²(2x)dx can be evaluated using integration by parts of the form ∫udv - ug - ∫vdu. Let uv = f(x) of the given integra expression determine the value of f(x) for x=0.44 (use radian form in 2 decimal places)
Answers
To determine the value of f(x) for x = 0.44 in the integral expression ∫xcos²(2x)dx, where uv = f(x) is used for integration by parts, we can let u = x and dv = cos²(2x)dx.
Integration by parts formula is given as ∫udv = uv - ∫vdu. In this case, we can let u = x and dv = cos²(2x)dx. This gives us du/dx = 1 and v = ∫cos²(2x)dx.
To find v, we can use the identity cos²(2x) = (1/2)(1 + cos(4x)). Thus, v = ∫(1/2)(1 + cos(4x))dx = (x/2) + (1/8)sin(4x) + C, where C is the constant of integration.
Now, we can use uv = f(x) to determine the value of f(x) for x = 0.44. This gives us f(0.44) = x[(x/2) + (1/8)sin(4x)] evaluated at x = 0.44.
Substituting x = 0.44, we get f(0.44) = 0.44[(0.44/2) + (1/8)sin(1.76)].
Evaluating sin(1.76) using radian form in 2 decimal places, we get sin(1.76) ≈ 0.97.
Substituting this value, we get f(0.44) ≈ 0.242. Therefore, the value of f(x) for x = 0.44 in the given integral expression is approximately 0.242.
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What will make the equation true? -4.1 - ___= -2 ½
Answers
Answer:
1.6
Step-by-step explanation:
Use this tax table to find how much tax you need to pay on a taxable income of $40,000.
If taxable
But not
The tax ls:
income is over- ovCr
SO
$7,825
10 percent of the
amount over SO
S7,825
$31,850
$782.50 plus 15 percent
of the amount over
7,825
$31,850
$77,100
$4,386.25 plus 25
percent of the amount
over 31,850
$77,100
$160,850 $15,698.75 plus 28
percent of the amount
over 77,100
$160,850
$349,700 $39,148.75 plus 33
percent of the amount
over 160,850
$349,700
no limit
$101,469.25 plus 35
percent of the amount
over 349,7
Answers
9514 1404 393
Answer:
$6,423.75
Step-by-step explanation:
The table tells you ...
If the amount is over 31,850 but not over 77,100 the tax is 4386.25 +25% of (40,000 -31,850).
So, the tax is ...
$4,386.25 + 0.25(40,000 -31,850) = $4,386.25 + 0.25(8,150)
= $4,386.25 +2,037.50 = $6,423.75
Match the pairs of equivalent expressions.
(-14+3/2b)+(1+8/2b)
4b+13/2
(5+2b)+(2b+3/2)
8b-15
(7/2b-3)-(8+6b)
-5/2b-11
(-10+b)+(7b-5)
-15-5/2b
Answers
The pairs of equivalent expressions matched together are;
(-14+3/2b)+(1+8/2b) = -15-5/2b
(5+2b)+(2b+3/2) = 4b+13/2
(7/2b-3)-(8+6b) = -5/2b-11
(-10+b)+(7b-5) = 8b-15
Which pairs of expressions are equivalent?Following PEMDAS
P = parenthesis
E = Exponents
M = Multiplication
D = Division
A = Addition
S = subtraction
(-14+3/2b)-(1+8/2b)
open parenthesis
= -14 + 3/2b - 1 - 8/2b
combine like terms
= -15 + 3/2b - 4b
= -15 + (3b-8b)/2
= -15 + 5/2b
(5+2b)+(2b+3/2)
open parenthesis
= 5 + 2b + 2b + 3/2
= 4b + (10+3)/2
= 4b + 13/2
(7/2b-3)-(8+6b)
= 7/2b - 3 - 8 - 6b
= (7b-12b)/2 -11
= -5/2b - 11
(-10+b)+(7b-5)
= -10 + b + 7b - 5
= -15 + 8b
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You buy a total of 100 turkey burgers and the veggie burgers cost 120. You pay 2 dollars per turkey burgers and. 5 dollars per veggie burger. Find the number of turkey and veggie burgers you buy. Find the slope intercept form show your work
Answers
Let's assume the number of turkey burgers is represented by 'x', and the number of veggie burgers is represented by 'y'. We are given two pieces of information: the total number of burgers is 100, and the cost of veggie burgers is $120. Based on this, we can set up the following system of equations:
x + y = 100 (equation 1)
2x + 5y = 120 (equation 2)
In equation 1, we have the total number of burgers, which is 100. In equation 2, we multiply the cost per turkey burger ($2) by the number of turkey burgers (x), and multiply the cost per veggie burger ($5) by the number of veggie burgers (y), and set it equal to the total cost of veggie burgers, which is $120.
To solve this system of equations, we can use any appropriate method such as substitution or elimination. Let's use the elimination method to solve the system:
Multiply equation 1 by 2 to make the coefficients of 'x' in both equations equal:
2x + 2y = 200 (equation 3)
Now subtract equation 3 from equation 2:
2x + 5y - (2x + 2y) = 120 - 200
3y = -80
Divide both sides by 3:
y = -80/3
Substitute the value of y into equation 1:
x + (-80/3) = 100
x = 100 + 80/3
x = 380/3
Therefore, the number of turkey burgers is approximately 126.67, and the number of veggie burgers is approximately -26.67. Since the number of burgers cannot be negative, we round these values to the nearest whole numbers.
Hence, the number of turkey burgers you buy is 127, and the number of veggie burgers you buy is 0.
Now, let's find the slope-intercept form of the equation. The slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.
From equation 1, we can rewrite it in slope-intercept form as:
y = -x + 100
Therefore, the slope-intercept form of the equation is y = -x + 100.
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which of the following statements do you believe are true? in a normal distribution - a) approximately 70% of the values are within one standard deviation from the mean, b) twenty-seven percent of the values are between one and two standard deviations from the means. c) 2.1% of the values are between -2 and -3 standard deviations from the mean. d) .1% of the values are 3 of higher standard deviations from the mean. e) all the alternatives are correct. f) none of the alternatives are correct. g) only a and b are correct. h) only c and d are correct.
Answers
The correct statement is "only a and c are correct" so option g is the answer.
The statement that is true in a normal distribution is "approximately 70% of the values are within one standard deviation from the mean" (a), and "2.1% of the values are between -2 and -3 standard deviations from the mean" (c).
These statements are true because of the properties of a normal distribution, also known as a Gaussian distribution or bell curve. In a normal distribution, the majority of values cluster around the mean, with fewer and fewer values as you move further away from the mean.
The statement "twenty-seven percent of the values are between one and two standard deviations from the mean" (b) is not true, as the correct percentage is approximately 27.7% (68-95-99.7 rule).
The statement "0.1% of the values are 3 or higher standard deviations from the mean" (d) is also not true, as the correct percentage is approximately 0.3%.
Therefore, the correct statement is "only a and c are correct".
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Simplify this expression:
\(7xy - x^{2}t+4xy+5x^{2}t\)
Answers
Answer:
\(11xy+4x^{2} t\)
Step-by-step explanation:
1. Collect Like Terms
\((7xy+4xy)+(-x^{2} t+5x^{2} t)\\\)
2. Simplify.
\(11xy+4x^{2} t\)
8. Given P = {vowels) and Q= {consonants), what is PU Q?
(a) PUQ = 0
(b) PU Q = {a, e, i, o, u}
(c) PU Q = {consonants}
(d) PU Q = {The English alphabet}
please answer urgent I'm timed please.....
Answers
Answer:
d) PU Q = {The English alphabet}
Step-by-step explanation:
because U means Union of all P and Q
the lower class limit represents the smallest data value that can be included in the class.True/False
Answers
the lower class limit represents the smallest data value that can be included in the classThe statement is true.
The lower class limit is the smallest value that can be included in a class interval.
Therefore, the statement is correct.
The lower class limit represents the smallest data value that can be included in a particular class. In a frequency distribution table, data values are grouped into classes, and each class has a lower and upper class limit. The lower class limit denotes the lowest value within that class, and any data value equal to or greater than the lower limit but less than the upper limit falls into that class.
The statement is true, as the lower-class limit indeed represents the smallest data value that can be included in the class.
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.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
Answers
The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.
What is the computation for the above solution?
Note that this is simple probability.
Hence probability of the 75% football starts selected randomly where the chance is 93% =
75% x 93%
= 69.75%
What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:
Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.
Recall that the total population is 100%.
Are these are independent or dependent events. Are they Inclusive or exclusive?From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.
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Suppose that ab = 5 cm. If we continually duplicated segment ab, what are the lengths of the first four segments you would be able to construct?
Answers
After solving the arithmetic sequences, he lengths of the first four segments will be 20 cm.
What is arithmetic sequences?Arithmetic sequences take the following format: a, a+d, a+2d, a+3d, etc. up to n terms. A is the first term; d is a frequent difference; and n is the total number of terms.
Find the AP, the number of terms, and the common difference for the calculation using the arithmetic sequence formulas. To determine the nth term, sum, or common difference of a given arithmetic sequence, various arithmetic series formulas are used.
To find the lengths of the first four segments we use the Arithmetic progression formula that is
\(a_n =\) a₁ + (n - 1)d
Where
an = the nᵗʰ term in the sequence
a₁ = the first term in the sequence
d = the common difference between terms
We have a₁ as 5 cm and as it is being duplicated the common ration d is 5
and we have been asked the length of the first four segments, so n = 4
Lets substitute the given information
\(a_n =\) 5 + (4 - 1)5
= 5 +(3)5
= 5 + 15
= 20
Thus, after continually duplicated segment ab, the lengths of the first four segments will be 20Cm
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A function is defined by the points {(0,2), (2,3), (5,9), (7,2)}. Which ordered pair can we add to the set to keep it a function?
Answers
Answer:
Choose 0 to substitute in for x to find the ordered pair. Remove parentheses. Simplify 3(0)−10 3 ( 0 ) - 10 .
Step-by-step explanation:
how to find local max and min from graph of derivative
Answers
When finding local maxima and minima from the graph of a derivative, we need to identify the points where the derivative changes sign. These points represent the locations of local maxima and minima on the original function.
Finding local maxima and minima from the graph of a derivativeWhen finding local maxima and minima from the graph of a derivative, we need to understand the relationship between the original function and its derivative. The derivative of a function represents the rate of change of the function at any given point. Local maxima and minima occur where the derivative changes sign from positive to negative or from negative to positive. At these points, the slope of the original function changes from increasing to decreasing or from decreasing to increasing.
Steps to find Local Maxima and Minima:Find the critical points by setting the derivative equal to zero and solving for x.Determine the intervals on the x-axis where the derivative is positive or negative.Use the first derivative test to determine whether each critical point is a local maximum or minimum.Check the endpoints of the interval to see if they are local maxima or minima.By following these steps, we can identify the local maxima and minima from the graph of a derivative.
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Identify the critical points, Determine the intervals, Analyze the sign changes and Check the endpoints
To find the local maximum and minimum points from the graph of a derivative, you can follow these steps:
Identify the critical points: These are the points where the derivative is either zero or undefined. Find the values of x where f'(x) = 0 or f'(x) is undefined.
Determine the intervals: Divide the x-axis into intervals based on the critical points and any other points of interest. Each interval represents a section of the graph where the derivative is either positive or negative.
Analyze the sign changes: Within each interval, observe the sign of the derivative. If the derivative changes sign from positive to negative, there is a local maximum at that point. If the derivative changes sign from negative to positive, there is a local minimum at that point.
Check the endpoints: Also, check the derivative's sign at the endpoints of the graph. If the derivative is positive at the leftmost endpoint and negative at the rightmost endpoint, there is a local maximum at the left endpoint. Conversely, if the derivative is negative at the leftmost endpoint and positive at the rightmost endpoint, there is a local minimum at the left endpoint.
By following these steps and analyzing the sign changes of the derivative within intervals, as well as checking the endpoints, you can identify the local maximum and minimum points from the graph of the derivative.
Learn more about: local maximum
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