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

a. f(x) is 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

a, d

It is evident from the graph of f(x) that

$f(x)= \begin{cases}1, & x \geq 1 \\ x^3, & x<1\end{cases}$

Clearly, f(x) is everywhere continuous but it is not differentiable at x = 1.