Question

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.

Answer 1

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 ...