28 Answered Questions for the topic Mean Value Theorem

Mean Value Theorem Calculus

03/23/22

Find the value or values of c that satisfy the equation f(b)-f(a)/b-a = f’(c) in the conclusion of the Mean Value Theorem for the function and intervals.

Find the value or values of c that satisfy the equation f(b)-f(a)/b-a = f’(c) in the conclusion of the Mean Value Theorem for the function and intervals.g(x) = {x³, -2 ≤ x ≤ 0; x², 0 < x ≤ 2
Mean Value Theorem Calculus Derivative

11/01/21

If the speed limit is 60 mph, can the police cite you for speeding.

At 10:17 am you pass a police car at 55 mph that is stopped on the freeway. You pass a second police car at 55 mph at 10:53 am, which is located 39 miles from the first police car. If the speed... more
Mean Value Theorem

01/29/19

AP Calculus AB; Mean Value Theroem homework

Hey guys, I am in AP Calculus and, so far, I finish like 85-90% of my work, but I am stuck with two questions, which is mainly about Mean Value Theorm, and I thought it gonna be easy and fast. But,... more

01/15/19

How is sin (5π/4) - cos (5π/4) = 0

In the question verify rolles theorem for the function f(x) = e^x ( sin x - cos x ) on [π/4, 5π/4],I can't understand why sin (5π/4) - cos (5π/4)=0?
Mean Value Theorem

09/03/18

if the mean of the data set 12, 19, 2, 4, 11 and x is 11 , what is the value of x?

I don't know how to answer this . how would I go about finding the value of x?
Mean Value Theorem

04/23/18

Let f(x) = (x − 3)^−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1).

Could someone please solve for c? I have solved it and I get c is equal to 7 but apparently it is wrong.    Thank you
Mean Value Theorem

04/22/18

Mean Value Theorem; f(x) = e^(-4x) on the interval [0,2]

Can somebody please help me find the value where f'(c)= f(b)-f(a)/b-a   I know f(x) does satisfy the hypothesis for the mean value theorem and the the derivative is -4e^(-4x)   How do I solve... more
Mean Value Theorem

05/29/17

((x^2)/2)-3x-(1/2);[4,6]

how to do this problem
Mean Value Theorem

02/09/17

Need help with a mean value theorem problem

Does the Mean value theorem apply to the given function on the given interval? Is so, find "c". If not, why not? f(x) = x - sin(pi x), [-1,1]
Mean Value Theorem

03/24/16

Mean Value Theorem

Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x³ - 4x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem
Mean Value Theorem

11/27/15

y = - x ^2/ 2 + x - 1/ 2 ; [-2, 1] , find the value of c that satisfies the mean value theorem

I am trying to understand this calculus problem but I am stuck. Please help me.
Mean Value Theorem

08/26/15

mean value theorem

let f(x)= x3 + 3x2 -10x , so that f(1)= -6 and f(2)= 0. by the mean value theorem, there exist a number y in the open interval (0,1) such that f ’(1+y) = 6. the value of y turns out to be  a)... more
Mean Value Theorem Calculus Ap Calculus

08/11/15

application of mean value theorem

The function f(x)= x(2/3)  on [-8,8] does not satisfy the conditions of the mean-value theorem because... A. f(0) is not defined.         B. f(x) is not continuous on [-8,8].              C. f ‘... more
Mean Value Theorem Calculus 1

08/02/15

Mean Value Theorem

a.) Verify that the hypotheses of the Mean Value Theorem are satisfied for each of the functions on the given interval, and b.)find the value of "c" which Mean Value Theorem... more
Mean Value Theorem Calculus

06/21/15

MEan value Theorem help!?

Verify that the hypotheses of the Mean Value Theorem are satisfied for each of the functions on the given interval, and find the value of "c" which Mean Value Theorem guarantees. f(x)= 4 − √x on... more
Mean Value Theorem Calculus Slope Derivatives

05/27/15

MEAN VALUE THEOREM AND AVERAGE SLOPE

Consider the function f(x)=8sqrt(x)+7 on the interval [36] . Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open... more
Mean Value Theorem Slope Math Help Derivatives

05/27/15

Consider the function f(x)=8sqrt(x)+7

Consider the function f(x)=8sqrt(x)+7 on the interval [36] . Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open... more
Mean Value Theorem

12/30/14

how to find mean value theorem?

is there any condition that f(a) and f(b) must equal thn we will find f'(c)?.otherwise not  
Mean Value Theorem Math Calculus Math Question

11/05/14

HELP HELP HELP

Cosider the quadratic function f(x) = Ax2 +Bx +C, where A,B,and C are real numbers with A≠ 0. Show that when the Mean Value Theorem is applied is applied to f on the interval [a,b],the number c... more
Mean Value Theorem Inequalities Inequality Derivatives

11/04/14

Finding f'(c) With an Inequality

Suppose that f'(x)≤2 for 2≤x≤4. Show that f(4)-f(2)≤4. Assume that f does satisfy the conditions of the Mean Value Thereom on the interval [2,4].  I'm using f(b)-f(a)/b-a=f'(c). So I'm assuming... more
Mean Value Theorem Calculus Derivatives

10/12/14

Mean Value Theorem Help!

Verify the function f(x)=1/x satisfies the hypothesis of the mean value theorem on [1,3]. Then find all numbers c that satisfy the conclusion of the mean value theorem.
Mean Value Theorem

04/03/14

mean value theorem

find the value(s) of c that satisfy the mean value theorem for the given function and interval.   f'(x)= √(x-3)   [3,8]

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