so, you want maximum f(p)
f'(p) = -9.02p+8
where f'(p)=0 is the maximum population.
of course, you can find the vertex of a parabola without calculus, but that's the sissy way ...
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p^2 + 8p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
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