Question

The total number of local maxima and local minima of the function $f\left(x\right)=\{\begin{array}{cc}{(2+x)}^3,& -3<x\le -1\\ x^{2/3},& -1<x<2\end{array}$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

$f\left(x\right)=(2+x{)}^3,-3=x^{2/3},-1$ $f^{\prime }\left(x\right)=3(2+x{)}^2,-3=2/3x^{-1/3},-1$, clearly $x=-2$ is extremum and at $x=-1$, $f\left(x\right)$ is not differentiable
Hence there is $2$ maximum or minimum point.