Is there any theorem that states something about the monotony of a product of functions? Let's say $f$ and $g$ are stictly increasing on $\mathbb R$. Does this mean that $f\cdot g$ is strictly increasing on $\mathbb R$ ? If case it's not, what if $f$ and $g$ are positive (or negative) on $\mathbb R$ ?
Monotony of product of functions
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monotone-functions
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0Try $f(x) = x$, $g(x) = x$. – 2017-02-10
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0@quasi What if $f$ and $g$ are positive ? – 2017-02-10
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1If $f,g$ are each increasing and also positive, then yes, the $f\cdot g$ is increasing. – 2017-02-10
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0@quasi And if they are both negative and increasing it also applies? – 2017-02-10
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1Apply the _definition_ of increasing. Suppose $f,g$ are increasing and positive. Suppose $a < b$. Then what can you say about $f(a)$ and $f(b)$? Same question for $g(a)$ and $g(b)$. Can you multiply those inequalities? Positivity of $f,g$ is relevant for that last question. – 2017-02-10
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0You have more than enough hints. Try to finish it. – 2017-02-10