What is the advantage of proving that a function is strongly quasiconcave?

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I have a function $f(x)$ which under certain conditions is strongly quasiconcave while under some other conditions it cannot be said whether the function is quasiconcave or not. If I am interested in finding the maxima of the function $f(x)$ then I can take the first derivative of $f(x)$ and check all of its roots. Whichever root gives me the highest value I can chose it as the maxima. So my question is why one should prove that under certain conditions the function is strongly quasiconcave (that is it has only one local maxima)? Can this proof affect the implementation of the algorithm for finding the global maxima of the function $f(x)$?