If $f(x)=a+b|x|+c|x|^4$, where $a, b, c$ are real constants, then $f(x)$ is differentiable at $x=0$

Question

If $f(x)=a+b|x|+c|x|^4$, where $a, b, c$ are real constants, then $f(x)$ is differentiable at $x=0$ if

Professor PC Thomas Classes · Answer

$|x|$ is non-differentiable at 0, whereas $|x|^4 = x^4$ is. For $f(x)$ to be differentiable at 0, coefficient of $|x|$ must be 0 ($b=0$).