Question

If $f\left(x\right)=min\{1,x^2,x^3\}$, 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
• D. f(x) is not differentiable at one point

Answer 1

The correct option is D f(x) is not differentiable at one point

$f\left(x\right)=x^3$, When $x<1$

and $f\left(x\right)=1$, When $x\ge 1$

$\therefore f\left(x\right)$ is not differentiable at $x=1$