37. Let $f(x) = \frac{1}{x}$ and $g(x) = \begin{cases} \frac{1}{x} & \text{if } x > 0\\ 1 + \frac{1}{x} & \text{if } x < 0 \end{cases}$ Show that $f'(x) = g'(x)$ for all $x$ in their domains. Can we conclude from Corollary 7 that $f - g$ is constant?
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For x > 0, g'(x) = -1/x^2 For x < 0, g'(x) = -1/x^2 Show more…
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