question_answer

Let \[h(x)=\min \,\{x,{{x}^{2}}\},\] for every real number of x,  Then

A) h is continuous for all x

B) h differentiable for all x

C) \[h'(x)=2,\]for all \[x>1\]

D) h is not differentiable at three values of x.

Correct Answer: A

Solution :

From the figure it is clear that From the graph it is clear that h is continuous for all \[x\in R,\] \[h'(x)=1\] for all \[x>1\] and h is not differentiable at \[x=0\]and 1.