For a logistic model with

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

For a logistic model

\dfrac{dQ}{dt}=kQ(L-Q)

with

k,L>0

, let

G(Q)=\dfrac{dQ}{dt}

. A student differentiates

G

with respect to

t

and finds

\dfrac{dG}{dt}=k^{2}Q(L-Q)(L-2Q)

. For which value of

Q

does

G

change from increasing to decreasing? (a)

\dfrac{3L}{4}

(b)

\dfrac{L}{2}

(c)

L

(d)

\dfrac{L}{4}