"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.)
f (x) = cos(πx/2)
Answers
Answer: The derivate is f'(x) = -sin(πx/2)*(π/2)
Step-by-step explanation:
We want the value of the derivate at each point marked:
As you may know, the derivate of cos(x) is equal to -sin(x)
And in our case:
f(x) = cos(πx/2)
f'(x) = -sin(πx/2)*(π/2)
Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))*g'(x)
Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:
f'(0) = -sin(π*0/2)*(π/2) = -sin(0)*(π/2) = 0
f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0
So this makes sense.
Related Questions
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
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multiply first equation by 3 and subtract it from second.
it will become
3x + 3y = 72
after subtracting from second we get:
2y = 28
y = 14
x = 24 - 14 = 10
We can conclude that there are more 5 points question. there are 10 three point questions and 14 five point questions.
Which of the points shown below are on the line given by the equation y = x - 1? Check all that apply.
A. Point A: (1, -2)
B. Point B: (2, 1)
C. Point C: (4, 3)
D. Point D: (-3, -4)
Answers
Final answer:
To find points on the line y = x - 1, substitute the x and y values of each point into the equation. Points B, C, and D satisfy the equation.
Explanation:
The equation given is y = x - 1. To determine which points lie on this line, you need to substitute the x and y values of each point into the equation and see if the equation holds true.
Point A: (1, -2) - Substitute x = 1, y = -2 into y = x - 1. -2 = 1 - 1 is false.Point B: (2, 1) - Substitute x = 2, y = 1 into y = x - 1. 1 = 2 - 1 is true.Point C: (4, 3) - Substitute x = 4, y = 3 into y = x - 1. 3 = 4 - 1 is true.Point D: (-3, -4) - Substitute x = -3, y = -4 into y = x - 1. -4 = -3 - 1 is true.Therefore, Points B, C, and D lie on the line represented by the equation y = x - 1.
The lengths of the sides of a triangle are 3x, 5x – 12, and x + 20. Find the value of x so that the triangle is isosceles. ...?
Answers
Any two side are equal in isoscles triangle
5x-12=x+20
4x=32
x=8
5x-12=28
x+20=28
5x=40
28,28,40
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Final answer:
To find the value of x for the triangle to be isosceles, we set the lengths of any two sides equal to each other and solve for x. After testing different cases, we find that x equals 10 satisfies the condition for the triangle to be isosceles.
Explanation:
For a triangle to be isosceles, at least two sides must have equal length. We're given the side lengths as 3x, 5x - 12, and x + 20. We have two cases to consider to find the value of x for the triangle to be isosceles:
Case 1: 3x = 5x - 12
Case 2: 3x = x + 20 or 5x - 12 = x + 20
To solve for x in case 1, we equate the two expressions and solve as follows:
3x = 5x - 12
2x = 12
x = 6
However, if we substitute x = 6 into the third side (x + 20), we get a length of 26, which does not equal either of the first two sides. Therefore, x = 6 does not satisfy the condition for an isosceles triangle.
For case 2, we consider 3x = x + 20:
3x = x + 20
2x = 20
x = 10
By substituting x = 10 into 5x - 12, we get 50 - 12 = 38. We can see that two sides of the triangle are 30 and 30 (since 3x equals 3(10)), confirming that the triangle is isosceles with x equal to 10.
How many solutions are there to the equation below?
11x + 25 = 7x + 15
A.
0
B.
Infinitely many
C.
1
D a monky beats a man with a stick
Answers
Answer:
D) A monky beats a man with a stick.
Step-by-step explanation:
Monky like stick. Monky like beat man.
Find The Distance Between (6,1) and (-2,-4)
Answers
How can you write 23/3 as a mixed number?
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What is the sum?
7/2+(-3/5)
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0.63 =1.00 0.634 plus what equals a dollar
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0.63 + 0.37 = 1.00
I hope I was somewhat helpful~
Best Regards~ Sans
or round it to 0.37
"In ABC, mBAC = 5x + 8, mABC = 6x + 22, and mBCA = 3x 25.
A.Find the value of x.
B.Find the measure of 3. Show your work."
Answers
Actually, the answer is 12.5
5x+8+6x+22+3x+25= 180
(5x+6x+3x)+(8+22-25)= 180
14x+5=180
14x+(5-5)=180-5
14x=175
14x/14=175/14
X=12.5
Double check:
(5*12.5)+8=70.5
(6*12.5)+22= 97
(3*12.5)-25=12.5
70.5+97+12.5=180 degrees.
So, x=12.5
Which of the following correctly expresses the number below in scientific notation? 0.00000765
A. 7.65 • 10-6
B. 7.65 • 10-7
C. 7.65 • 10-5
D. 76.5 • 10-7
E. 765 • 10-8
F. 765 • 10-6
Answers
Should be 7.65 * 10^-6
In scientific notation, 0.00000765 is written as 7.65 • 10-6. This represents the number of places to the right of the decimal point to the first non-zero digit.
Explanation:The task is to express the number 0.00000765 in scientific notation. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in standard decimal form. It is commonly used in science and mathematics.
We have to determine which of the given options correctly represents this number in scientific notation.
The number 0.00000765 can be written as 7.65 times ten to the negative sixth power. This is because there are six places to the right of the decimal point before we encounter the first non-zero digit. Therefore, the correct answer is 7.65 • 10-6.
Learn more about scientific notation here:
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jacob has exactly 84 cents in his pocket.he only has dimes and quartere. how many pennies does he have if he has 3 dimes
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3 times 10=30
30 cents are dimes
84=dimes+quarters
84=30+quarters
minus 30
54=quartesr
that can't be right
quartesr go like this
1 quarter=25
2 quarter=50
3 quarters=75
maybe there are pennies even though a penny is neither a dime nor a quarter
2 quarters make 50
4 pennies make the last 4
I guess 4 pennies
Common factors of 32 and 40
Answers
40=2^3.5
common factors=2^3=8
Reduce this algebraic fraction 27c^4d^5/9c^7d^4 ...?
Answers
The fraction is: [tex] \frac{27 c^{4} d^{5}}{9 c^{7} d^{4} } [/tex]
Let's rewrite it: [tex]\frac{27 c^{4} d^{5}}{9 c^{7} d^{4} }= \frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }[/tex]
Now, let's use the rule [tex] \frac{ x^{a} }{ x^{b}} = x^{a-b} = \frac{1}{ x^{b-a} } [/tex]:
[tex]\frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }=3* \frac{1}{c^{7-4}} * d^{5-4} =3* \frac{1}{ c^{3} } *d^{1}= \frac{3d}{ c^{3} } [/tex]
which even number is not a composite number2, 8, 4, 6
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The price of a pair of shoes increases from $51 to$69. what is the percent increase to the nearest percent?
Answers
Answer:
35%
Step-by-step explanation:
A fast food restaurant sells between 164 and 328 hamburgers per day. If the company profits $82.00 per 82 hamburgers sold, approximately how much does the company profit in one year from hamburgers?
PLZZZZZZ HELPPPP !!!!!!!!!!
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Approximate profit in one year from hamburgers will be $59860 to $119720.
What is unitary method?The unitary method is used to find the value of a single unit from a given multiple
How much does the company profit in one year from hamburgers?A fast food restaurant sells between[tex]164[/tex]and [tex]328[/tex] hamburgers per day. If the company profits [tex]$82.00[/tex] per [tex]82[/tex] hamburgers sold which mean they make [tex]$1[/tex] profit for one unit of burger sold.
Thus a year being of [tex]365[/tex] days the profit the company will make after selling [tex]164[/tex] to [tex]324[/tex] units of burger will be $59860 to $119720.
Learn more about profit here:
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Which is not a property of all similar triangles
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Molly runs each morning once around a circular path in her neighborhood. if the diameter of the path is 1.4 miles, how far does molly run each day?
Answers
Formula for circumference = pi multiplied by the diameter
So you simply do:
pi multiplied by 1.4 miles
And you should get:
4.39822971503... miles
Simply round the result to an appropriate value (e.g. 3 decimal places).
Answer: 4.398 miles (to 3dp)
Hope the answer helps :)
for questions 1-2, find the x- and y-intercept of the line.
1. -10x+5y+40
a) x-intercept is 5; y- intercept is -10
b) x-intercept is 8; y-intercept is -4
c) x-intercept is -10; y-intercept is 5
d) x-intercept is -4; y-intercept is 8
2. 5x+4y=80
a) x-intercept is 4; y-intercept is 5
b) x-intercept is 20; y-intercept is 16
c) x-intercept is 5; y-intercept is 4
d) x-intercept is 16; y-intercept is 20
Answers
1 is c and 2. is d
two numbers that multiply to 120 and add to 29
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Fill in the blank:
To find the values of p, q, r and s, you should start by finding all factor ___ of the leading coefficiant and constant term. Then try them to determine which ones give you the correct product ...?
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Graph x2 + 9y2 = 25. What are the domain and range?
Someone please help me !
(Picture below)
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x^2/5^2 + (3y)^2/5^2 = 1
This represent an equation of an ellipse with cente at the origin, the horizontal major axis running from -5 to 5 and vertical minor axis running from -5/3 to 5/3
The third graph is the correct answer.
Answer:
the third graph is correct.
Step-by-step explanation:
domain: -5 ≤ x ≤ 5
range: -1.67 ≤ y ≤ 1.67
simplify this expression 1x/18x
Answers
Answer: 1/18
Step-by-step explanation: The x's basically cancel each other out so all that is left is the 1 and the 18
Given: x + y = 15. Which of the following are ordered pairs of this equation?
Answers
(0-5) (1-4) (2-3)
A Branliest or just a thanks would be terrific!
Quadrilateral MNOP is a rhombus. Find the measure of angle MRN.
a. 90
b. 45
c. 85
d. 60
Answers
Without further information or a diagram indicating the position of point R in the rhombus MNOP, we cannot accurately determine the measure of angle MRN. If R is at the intersection of the diagonals, angle MRN would be 90 degrees.
Explanation:The student asks to find the measure of angle MRN in a rhombus named MNOP. Unfortunately, the information provided is insufficient to determine the measure of angle MRN directly. However, one property of a rhombus is that all sides are of equal length and opposite angles are equal. Additionally, the diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Without a specific diagram or more information about the location of point R in relation to the rhombus, it's impossible to give an exact answer. If R is located at the center where the diagonals intersect, then angle MRN would be 90 degrees because the diagonals of a rhombus bisect each other at right angles. If R is not at the center, then we cannot determine the angle without additional information.
WILL UPVOTE
This is all the info it gives me so sorry.
The formula for rate is r=dt.
Solve for d.
Enter your answer in the box.
Thanks!
Answers
Which relation is a direct variation that contains the ordered pair (2, 7)?
Y=4x-1
y=2/7x
y=7/2x
y=7/x
Answers
y = kx + n
Direct variation in simple is equation of a line which has n=0 or in other words which y to x ratio is k.
First option gets 7=7 but it isnt direct variation because n is not equal to 0
third option is indeed correct. once we implement coordinates (2,7) we get 7=7
Answer is
y = 7/2x
Answer: The guy up above, is correct. The answer is D
Step-by-step explanation: Edge 2021
What is the relative maximum and minimum of the function?
f(x)=x^3+6x^2-36
The relative maximum is at (–6, 216) and the relative minimum is at (2, –40).
The relative maximum is at (–6, 40) and the relative minimum is at (2, –216).
The relative maximum is at (6, 216) and the relative minimum is at (–2, –40).
The relative maximum is at (6, 40) and the relative minimum is at (–2, –216).
Answers
f'(x)=3x^2+12x
find where it equals zero
it equal zero at x=0 and x=-4
find the y values
f(0)=-36
f(-4)=-4
the critical points are (0,-36) and (-4,-4)
make sign chart
evalutat f'(x) at x=-5 and x=-1 and x=1, and see their signs
f'(-5)=(+)
f'(-1)=(-)
f'(1)=(+)
see below attachment
max is where sign changes from (+) to (-)
min is where sign changes from (-) to (+)
so
max at (-4,-4)
min at (0,-36)
none of the options are correct, do you have te right problem?
at a local store you find the following prices listed:
Tape 2 rolls for $1.28
Notepads 3 pads for .87
Highlighters 1 for 1.59
Pens 2 for 1.98
How much would you pay for one roll of tape, two note pads, two highlighters, and two pens?
A. $8.07
B. $4.50
C. $6.38
D. $5.72
Answers
If P(x) = 2x 4 - x 2 + 3x - 1, use synthetic division to find P (2).
17
21
33
Answers
Answer: 33
Step-by-step explanation:
P(x) = 2x 4 - x 2 + 3x - 1
To find the value of p(2) we simply substitute x = 2.
That is; wherever you see x, simply put 2
P(2) = 2 [tex](2)^{4}[/tex] - [tex](2)^{2}[/tex] + 3(2) - 1
=2(16) - 4 + 6 - 1
= 32 - 4 + 6 -1
=28 + 6 -1
=34 - 1
=33
Therefore the value of P(2) is 33