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## Homework Statement

I have y=2x*f(x).

f is strictly monotonically decreasing, non-negative, derivable and continuous in the close interval [0,c] with c>=1. it doesn't change its concavity in the interval, maybe beside at x=c/2. Note that 2x has the same properties but is monotonically increasing.

i've found a maximum point for y, at x=c/2, but not knowing f i was able only to demostrate that it was a local max. i want to say that it's the global max

**2. The attempt at a solution**

if there's a unique maximum for y in the interval [0,c], then my local max is automatically the global max

i think that is obviously true, but does it exist a theorem that says

*the product of two nonnegative functions with fixed concavity, one monotonically increasing and the other decreasing in [a,b], is a function that has a single maximum point, being monotonically incresing before and monotonically decreasing after. if the max is in a or b then the new function is only increasing or decreasing*

or something like that?

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