Question

Differential Equation: dy/dt=(y-2)(4-y). On what intervals for y does the population grow? Decline? Which value of y gives the maximum rate of growth?

Answer 1

y grows when dy/dt > 0
decline when dy/dt < 0

maximum is achieved when dy/dt = 0 and before this specific value y was increasing
and after this specific value y is decreasing

Answer 2

i hope it helps ..

Answer 3

max OR min is when dy/dx = 0