# Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x)= 6 cos (x)#; [-pi/2, pi/2]?

##### 1 Answer

Jan 20, 2017

Please see below.

#### Explanation:

There is no "using the priciple of the mean-value theorem" (whatever that means) involved.

Write down what the conclusion of the theorem says:

There is a

#f'(c) = (f(pi/2)-f(-pi/2))/(pi/2-(-pi/2))#

Now do the calculus, algebra, and trigonometry needed to find

We can see that

and

So you need to solve

The only solution in the interval is