Question

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

• A. $f\left(x\right)$ is continuous $\forall xϵR$
• B. $f^{\prime }\left(x\right)>0$ $\forall x>1$
• C. $f\left(x\right)$ is not differentiable but continuous $\forall xϵR$
• D. $f\left(x\right)$ is not differentiable for two values of x

Answer 1

The correct option is A $f\left(x\right)$ is continuous $\forall xϵR$

From graph $f\left(x\right)$ is continuous for all $x$ and not differentiable at $x=1$ due to sharp edge