Question

The value of $m$ for which the function $\{\begin{array}{c}m{x}^2,x\le 1\\ 2x,x>1\end{array}$ is differentiable at $x=1$, is

• A. $0$
• B. $1$
• C. $2$
• D. $Dosenotexist$

Answer 1

The correct option is C $2$

For the function to be differentiable, it must be continuous at $x=1$

$\therefore$ $2x={mx}^2$ [at $x=1$]

$\Rightarrow$ $\therefore$ $m=2$ [$C$]