# 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)=x-cosx#; [-pi/2, pi/2]?

##### 1 Answer

Feb 17, 2017

See below.

#### Explanation:

I am unaware of anything that might be called "the principle of the MVT" that can be used to do this.

What we need is knowledge of what the conclusion of MVT says and enough algebra and trigonometry skills to solve an equation.

**Solution**

The conclusion of MVT for this function on this interval says:

there is a

Now do the calculus, trigonometry and algebra to find

This amounts to solving

So,