Can anyone help me to solving problem.

Is the following proposition right? Prove, if right. Give a counter example, if wrong.

Proposition: If $f$ is continuous at $x=0$ then $f^4$ is differentiable at $x=0$.

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Hint: If $g\colon \mathbb R \to [0,\infty)$ is continuous, but not differentiable at 0 (You know such a function, right?), what can you say about $\sqrt[4]g$?
Hint: Try $f:\mathbb R\to\mathbb R$, $x\mapsto|x|^a$, for some suitable $a\gt0$.