question_answer

If\[200\mu F\] 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)  (x) is not differentiable at one point

Correct Answer: D

Solution :

It is evident from the graph of r( x) that \[f(x)=\left\{ \begin{matrix}    1, & x\ge 1  \\    {{x}^{3}}, & x<1  \\ \end{matrix} \right.\] Clearly, f( x) is everywhere continuous but it is not differentiable at x = 1.