determine-whether-the-following-piecewise-function-is-differentiable-at-x1x-1x1-

Question

Determine whether the following piecewise function is differentiable at $x equals 0$ .

$g (x) = {\begin{matrix} 4 x + \sin x, if x < 0 \\ 2 x^{2}, if x \geq 0 \end{matrix}$

Accepted Answer

Answer

Determine whether the following piecewise function is differentiable at x=0x=0.g(x)={4x+sinx,if x<02x2, if x≥0g\left(x\right)=\begin{cases}4x+\sin x,\text{if }x<0\\ 2x^2,\text{ if }x\ge0\end{cases}