Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be respectively given by $f(x)=|x|+1$ and $g(x)=x^

Question

Let $f: R ightarrow R$ and $g: R ightarrow R$ be respectively given by $f(x)=|x|+1$ and $g(x)=x^{2}+1$. Define $h: R ightarrow R$ by $h(x)=\left\{\begin{array}{ll}\max \{f(x), g(x)\}, & 	ext { if } x \leq 0 \ \min \{f(x), g(x)\}, & 	ext { if } x>0\end{array}ight.$ The number of points at which $h(x)$ is not differentiable is

Professor PC Thomas Classes · Answer

(3) :\  From the given graph the function $h(x)$ in closed form is\ $h(x)= \begin{cases}x^{2}+1, & -\infty<x \leq-1 \ -x+1, & -1<x \leq 0 \ x^{2}+1, & 0<x \leq 1 \ x+1, & 1<x<\infty\end{cases}$\ Hence the points of non-differentiability are $-1,0$ and 1 .\