Consider the autonomous differential equation

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

Problem

\dfrac{dy}{dx}=y(y-4)

. A solution satisfies

0<y(0)<4

and remains in the interval

0<y<4

for some time. Which statement best describes the concavity of this solution while

0<y<4

? (a) The solution is concave up for all

0<y<4

because

\dfrac{d^2y}{dx^2}>0

throughout the interval. (b) The solution is concave down when

0<y<2

and concave up when

2<y<4

. (c) The solution is concave up when

0<y<2

and concave down when

2<y<4

. (d) The solution is concave up when

0<x<2

and concave down when

2<x<4