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

Question

Determine whether the following piecewise function is differentiable at x=0x=0.g(x)={4x+sin⁡x,if x02x2, if x≥0g\left(xight)=\begin{cases}4x+\sin x,	ext{if }x

Accepted Answer

No

Answer

Yes

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\(\ge\)0\(\end{cases}\)

Determine whether the following piecewise function is differentiable at $x equals 0$ .
$g (x) = {\begin{matrix} 4 x + \sin x, if x < 0 \\ 2 x^{2}, if x \geq 0 \end{matrix}$