# How do you find the value of c guaranteed by the Mean Value Theorem for #f(x)=(2x)/(x^2+1)# on the interval [0,1]?

##### 1 Answer

#### Explanation:

I would begin by checking that the hypotheses are true.

This function is continuous on

and differentiable on

so the hypotheses of the Mean Value Theorem are true.

**The conclusion of the Mean Value Theorem** is that there is a number

We have been asked to find the number(s) whose existence the theorem asserts.

For

Furthermore

We need to solve:

So

Complete the square or use the quadratic formula to solve for

Clearly

Again clearly, the negative root is not in