Question
Suppose that $f(x)$ and $g(x)$ are differentiable and positive everywhere. If $f^{\prime}(x)<0$ and $g^{\prime}(x)>0$ everywhere, show that $h(x)=f(x) / g(x)$ is a decreasing function.
Step 1
We are given that $f(x)$ and $g(x)$ are differentiable and positive everywhere. This means that their derivatives, $f'(x)$ and $g'(x)$, exist for all values of $x$. Show more…
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