Question

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

• A. $h$ is a continuous for all $x$
• B. $h$ is a differentiable 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)

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

From figure $h\left(x\right)$ is continuous for all x,
but $h\left(x\right)$ is not differentiable at two points $x=0$ and $x=1$
Also $h^{\prime }\left(x\right)=1,\forall x>1$