Question

If $f\left(x\right)=\{\begin{array}{c}1,x<0\\ x^2,x\ge 0\end{array}$ then at $x=0$

• A. $f^{\prime }$ is differentiable
• B. $f$ is continuous
• C. $f$ is differentiable
• D. $f$ is not continuous

Answer 1

Answer: (C)

$f$ is differentiable

$f^{\prime }\left(x\right)=0f^{\prime }\left(x\right)=2x$

$f^{\prime }\left(0\right)=0f^{\prime }\left(0\right)=0$

$\therefore f$ is differentiable at $x=0$