For the polynomial

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

For the polynomial

h(x)=x^{3}+3x-1

, answer the following: (i) Compute

h'(x)

. (ii) Prove that

h'(x)>0

for every real

x

. (iii) Deduce whether

h

possesses any local maximum or local minimum points. Justify your answer.