In studying how a predator forages a prey, an important concept is the functional response, defined as

where R is the prey population density, C is the attack rate constant, h is the handling time for a single prey, and t is the optimal foraging time, which is itself a function of R. A type-2 response, which is the type most commonly observed in the laboratory, is when the curve is concave down. Show that this occurs when

f(R) = tCR 1 + hCR'