question_answer

Let \[h(x)=\max \,\{-x,\,1,\,{{x}^{2}}\}\] for every real number \[x\]. Then,

A)  \[h\] is continuous for all \[x\]

B)  \[h\] is differentiable for all \[x\]

C)  \[h'(a)=1,\,\,\forall x>1\]c

D)  h is not differentiable at two values of \[x\]

Correct Answer: A

Solution :

 Now we draw the graph \[y=-x,\,\,y=1\] and \[y={{x}^{2}}\] From graph it is clear that \[h\,(x)\] is continuous at all \[x\] and it not differentiable at \[x=-1,\,\,0,1\].