Write the equation for the optimal prey density (the value giving the maximum rate of prey capture) in terms of F'(p). Find the optimal prey density if F(p) = p. Make sure to separately consider cases with c < 1 and c > 1.
Now suppose that the number of prey that escape increases linearly with the number of prey (the prey join together and fight back). Let p be the number of prey and F(p) be the functional response. The number of prey captured is then F(p) - cp. The constant c represents how effectively the prey can fight.