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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.

  • 0
    What have you tried? What is the definition of differentiable at $0$? (Technically $g$ doesn't need to be continuous at $0$, but at worst it can have a removable discontinuity there.)2012-12-09
  • 1
    Use the definition of derivative.2012-12-09

2 Answers 2