A function $f$ is defined on $[-3,3]$ as $f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}\righ

Question

A function $f$ is defined on $[-3,3]$ as $f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}ight\}, & -2 \leq x \leq 2 \ {[|x|],} & 2<|x| \leq 3\end{array}ight.$ where $[x]$ denotes the greatest integer $\leq x$. The number of points, where $f$ is not differentiable in $(-3,3)$ is

Professor PC Thomas Classes · Answer

(5) :\ $f(x)=\left\{\begin{array}{cc}\min \left\{|x|, 2-x^{2}ight\}, & -2 \leq x \leq 2 \ {[|x|],} & 2<|x| \leq 3\end{array}ight.$\ From the graph, we see that number of points of non-differentiability in $(-3,3)=5$.\