Question

х Discuss the applicability of Rolle's theorem for f (x) = x (2 + x) e 2 in (-3,0).​

Answer 1

Given the function f(x)=x2/3 on [−1,1].

Now, f(−1)=1=f(1).

Also the function is continuous in [−1,1].

But the given function is not differentiable at x=0.

Since,

h→0limhh32−0

=h→0limh311 does not exist.

So this function does not satisfy the Rolle's theorem on [−1,1].