In studying salmon populations, a model often used is the Ricker equation which relates the size of a fish population this year,

x to the expected size next year y. (Note that these populations do not change continuously, since all the parents die before the eggs are hatched.) The Ricker equation is

y = axe^(-bx) where a,b> 0

Find the value of the current population which maximizes the salmon population next year according to this model.

---> I differentiated it this far:

dy/dx = axe(-bx)(-b) + e^(-bx)(a)

dy/dx = -axe^(-bx)b + ae^(-bx)

dy/dx = 0 = ae^(-bx) (-xb + 1)

in the question we are given that a,b>0 Could anyone please tell me how to further solve this question??