1. The problem statement, all variables and given/known data Another model for a growth function for a limited pupulation is given by the Gompertz function, which is a solution of the differential equation dP/dt = c*ln(K/P)*P where 'c' is a constant and 'K' is the carrying capacity. At what value of P does P grow fastest? 2. Relevant equations c = .05 K=1000 P_0 = 500 (initial condition) P(t) = 1000/e^(e^(-.05t-.3665)) (this is the specific solution) 3. The attempt at a solution I think it is asking to find what the max value of dP/dt. However I think to do this, I need to find the derivative of dP/dt which is d^2P/dt^2 and set it equal to zero. This will let me find t when the slope of P is at its max and then I plug t back into P. Is this correct? If it is, I am in for one hell of a derivative... Thanks!