Question

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`?

The function is given as:

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

Answer 1

Rolle's theorem cannot be applied to this function.

Explanation:

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]}