# Given the function #f(x)=(x^2-1)/x#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?

##### 1 Answer

#### Explanation:

The Mean Value Theorem has two hypotheses:

**H1** :

**H2** :

In this question,

This function is a rational function, so it is continuous on its domain, but the domain does not include **The function does not satisfy the first hypothesis on this interval.**

(That is, there is at least one point in

Differentiability implies continuity, so non-continuity imples non-differentiability. **The function does not satisfy the second hypothesis on this interval.**

(That is, there is at least one point in

Although this function **does not** satisfy the hypotheses on the interval, it could satisfy the conclusion.

(For an example of a function that does not satisfy the hypotheses but does satisfy the conclusion, see https://socratic.org/questions/given-the-function-f-x-x-1-3-how-do-you-determine-whether-f-satisfies-the-hypoth )

Attempting to solve

#(x^2+1)/x^2 = 0#

This equation has no solution in the real numbers, so it has no solution in

There is no