# If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b)such that f '(c) = f(b)-f(a)/b-a. 1. f(x)=square root of 1-x, [-8,1] I understand that The mean...

If the Mean Value Theorem can be applied, find all values of *c* in the open interval

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### 1 Answer

The mean value theorem tells you that a certain slope is possible over an interval.

What this question is asking you is to find all the points (values of c) where this slope exists over the interval. There can be one or more points with the mean value theorem slope.

I will do another problem.

`f(x) = x^2` on the interval [-2, 1]

I find the slope between those two points (-2, 4) and (1,1)

`(4-1)/(-2-1) = -1`

I know there will be at least one point with slope -1.

`f'(x) = 2x`

I want to find all values of x where f'(x) is -1

`-1 = 2x`

x = -1/2

Therefore there is one value of c, and it is -1/2

Hope this helps you solve your problem!

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Yes, but what confuses me is the square root