Question: Let \(f\left( x \right)={{x}^{2}}\sin \left( \frac{1}{x} \right)\) for \(x\ne 0\), \(f\left( 0 \right)=0\). Apply the definition of the derivative to show that f is differentiable at x = 0, and \(f'\left( 0 \right)=0\).