Question

Asked Jan 20, 2020

1 views

Suppose that ƒ is continuous on [a, b] and that c is an interior point of the interval. Show that if ƒ′(x) <=0 on [a, c) and ƒ′(x)>= 0 on (c, b] , then ƒ(x) is never less than ƒ(c) on [a, b].

Step 1

__Mean Value Theorem__:

Step 2

Given that *f* is continuous on [*a*, *b*] and *c* is an interior point of the interval [*a*, *b*].

Then *f* is continuous on [*a*, *c*) and on (*c*, *b*].

Step 3

Also,

...Find answers to questions asked by student like you

Show more Q&A

Q: Can I get with this problem step by step?

A: To find: -

Q: Graph ƒ(x) = x ln x. Does the function appear to have an absolute minimum value? Confirm your answer...

A: Click to see the answer

Q: Graph the functions in Exercises 79–80. Then find the extreme values of the function on the interval...

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: find the function with the given derivative whose graph passes through the point P. 39. ƒ′(x) = 2x -...

A: The given derivative and the point is,

Q: The position at time t>= 0 of a particle moving along a coordinate line is s = 10 cos (t + pai/4)...

A: Given:

Q: You are planning to make an open rectangular box from an 8-in.by-15-in. piece of cardboard by cuttin...

A: Given you are planning to make an open rectangular box from an 8-in.by-15-in. piece of cardboard by ...

Q: Can I get with this problem step by step?

A: Given equation

Q: What is the derivative of the exponential function a x, a >0 and a ≠ 1? What is the geometric sig...

A: The derivative of the exponential function ax is as follows.

Q: a. Does cos 3x ever equal x? Give reasons for your answer. b. Use Newton’s method to find where.

A: Part A: Here the given trigonometric function is f(x) =x – cos 3x. In the given graph there are poin...