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Let  \mathrm{h(x)=\min \left|x, x^2\right|} , for every real number x. Then

Option: 1

h is continuous for x 


Option: 2

h is differentiable for all x


Option: 3

\mathrm{h^{\prime}(x)=1} , for all x>1


Option: 4

h is  differentiable at two values of  x


Answers (1)

best_answer

\mathrm{f(x)=\min \left(x, x^2\right)= \begin{cases}x, & x<0 \\ x^2, & 0 \leq x<1 \\ x, & x \geq 1\end{cases}}

is shown in the adjacent figure. It is evident from the graph that the given function is continuous for all x but not differentiable at x=0 and x=1. Also, \mathrm{ h^{\prime}(x)=1}  for all x>1.

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Ritika Harsh

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