Question: Verify that f satisfies the conditions of Rolle’s Theorem on the indicated interval and find all numbers c on the interval such that f '(c)=0.

(a) \(f\left( x \right)={{x}^{4}}-{{x}^{3}},\,\,\,\left[ 0,1 \right]\)

(b) \(f\left( x \right)=2\sin \left( \frac{1}{2x} \right),\,\,\,\left[ 0,\pi \right]\)