Question

The function $y=\frac{2-x^2}{x^4}$ takes on equal values at the end-points of the interval [-1, 1]. Is Rolle's theorem valid in this interval?

Answer 1

Given $y=f\left(x\right)=\frac{2-x^2}{x^4}$

$f\left(x\right)$ is a rational function and rational functions are continuous in its domain.

But since $f\left(x\right)$ is not defined at $x=0$

So, it is not continuous at $x=0$

Hence, Rolle's theorem is not applicable.