Determine whether Rolle's Theorem can be applied to $f$ on the closed interval $[a,b]$ . If Rolle's Theorem can be applied, find all the values of $c$ in the open interval $[a,b]$ such that $f^'(c)=0$ ?

Question

The function is given as:

f(x) = (x^2)/(1-x^2) , [-2,2]

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Answer 1 · 2017-09-25T09:46:34

Rolle's theorem cannot be applied to this function.

The function $f(x) = x^2/(1-x^2)$ is not continuous in the interval $x in [-2,2]$ , since the denominator vanishes for $x=+-1$ .

The hypotheses of Rolle's theorem are therefore not satisfied.

graph{ x^2/(1-x^2) [-10, 10, -5, 5]}