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
Answer & explanation
Correct answer: option 4
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.
