If $f(x)=\min \left\{1, x^2, x^3\right\}$, then

• A

  $f(x)$ is not everywhere continuous
• B

  $f(x)$ is continuous and differentiable everywhere
• C

  $f(x)$ is not differentiable at two points
• Correct answer
  D

  $f(x)$ is not differentiable at one point

Solution

It is evident from the graph of $f(x)$ that $f(x)=\left\{\begin{array}{cc}1, & x \geq 1 \\ x^3, & x \lt 1\end{array}\right.$ Clearly, $f(x)$ is everywhere continuous but it is not differentiable at $x=1$.

Hence, the correct answer is option: 'D'.