Question

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

• A. $h$ is continuous for all $x$
• B. $h$ is differential for all $x$
• C. $h^{\prime }\left(x\right)=1$, for all $x>1$
• D. $h$ is not differentiable at two values of $x$

Answer 1

Answer: (A), (C), (D)

$h^{\prime }\left(x\right)=1$, for all $x>1$
$h$ is not differentiable at two values of $x$
$h$ is continuous for all $x$

$h\left(x\right)=\{\begin{array}{c}x,x<0\\ x^2,0\le x\le 1\\ x,x>1\end{array}$
$h^{\prime }\left(x\right)=\{\begin{array}{c}1,x<0\\ 2x,0\le x\le 1\\ 1,x>1\end{array}$
Hence f is not differentiable at $x=0$ and $x=1$
Also f is continuous for all $x$