Let . The derivative satisfies and . Determine whether corresponds to a local…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

h(x)=x^{4}-4x^{3}

. The derivative satisfies

h'(0)=0

and

h''(0)=0

. Determine whether

x=0

corresponds to a local maximum, a local minimum, or neither for

h

, and justify your conclusion.