# How do you verify whether rolle's theorem can be applied to the function #f(x)=1/x^2# in [-1,1]?

##### 1 Answer

**not** satisfy the conditions of Rolle's Theorem on the interval

#### Explanation:

Rolle's Theorem states that if a function,

So what Rolle's Theorem is stating should be obvious as if the function is differentiable then it must be continuous (as differentiability

With

Differentiating wrt

To find a turning point we require;

# f'(x)=0 => -(2)/x^3 = 0#

Which has no finite solution. We can conclude that **not** satisfy the conditions of Rolle's Theorem on the interval

We can see that this is the case graphically, as f(x) has a discontinuity when

graph{1/x^2 [-10, 10, -2, 10]}