Question

Let $f\left(x\right)=\{\begin{array}{cc}min\{x,x^2\},& x\ge 0\\ max\{2x,x^2-1\},& x<0\end{array}$
Then which of the following is not true?

• A. $f\left(x\right)$ is continuous at $x=0$
• B. $f\left(x\right)$ is not differentiable at $x=1$
• C. $f\left(x\right)$ is not differentiable at exactly three points
• D. none of these.

Answer 1

The correct option is D none of these.

From graph it is clear that the function is continuous everywhere but not differentiable at three points where we can see peaks in graph
Hence the answer is "D"