Let $g:\mathbb{R}\rightarrow \mathbb{R}$ be continuous at $0$.
1.) Prove that $f(x)=xg(x)$ is differentiable at $0$ (via proof form).
2.) Briefly explain how/why the continuity of $g$ at $0$ was needed in part (a).
I'm not sure how.
Let $g:\mathbb{R}\rightarrow \mathbb{R}$ be continuous at $0$.
1.) Prove that $f(x)=xg(x)$ is differentiable at $0$ (via proof form).
2.) Briefly explain how/why the continuity of $g$ at $0$ was needed in part (a).
I'm not sure how.