Question

Let $f:R\to R$ be a function defined by $f\left(x\right)=max\left\{x,x^2\right\}$. Let $S$ denote the set of all points in $R$, where $f$ is not differentiable

• A. $\left\{0,1\right\}$
• B. $\left\{1\right\}$
• C. $\left\{0\right\}$
• D. an empty set

Answer 1

The correct option is A

$\left\{0,1\right\}$

Finding the non-differentiable point

Let's visualize the two given equations: $y=xandy=x^2$

We have drawn both the equation's graph. The curved graph belongs to $y=x^2$ and the straight line belongs to $y=x$.

Finding the point of intersection of the two graphs at their max:

$$\begin{gathered} x^2=x \\ \Rightarrow x^2-x=0 \\ \Rightarrow x(x-1)=0 \\ \Rightarrow x=0or1 \end{gathered}$$

The graph will have sharp points at $x=0andx=1$ and therefore, the f(x) will be non-differentiable at those points.

Hence, the correct answer is Option (A).