## Calculus: Early Transcendentals 8th Edition

$f'(x) = g'(x)~~~$ for all $x$ in their domains. We can not conclude from Corollary 7 that $f- g$ is constant.
The domain of $f$ is $(-\infty,0) \cup (0,\infty)$ The domain of $g$ is $(-\infty,0) \cup (0,\infty)$ $f'(x) = -\frac{1}{x^2}$ and $g'(x) = -\frac{1}{x^2}$ Thus $~~~f'(x) = g'(x)~~~$ for all $x$ in their domains. According to Corollary 7, in the interval $(-\infty,0)$: $f- g = c_1~~$ for some constant $c_1$ Also, according to Corollary 7, in the interval $(0,\infty)$: $f- g = c_2~~$ for some constant $c_2$ However, it is possible that $c_1 \neq c_2$ Therefore, we can not conclude from Corollary 7 that $f- g$ is constant.