For the differential equation

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

Problem

\dfrac{dy}{dx}=x^{2}-1

, the slope field shows negative slopes where

-1<x<1

and positive slopes elsewhere. Which initial point would yield a solution curve that is initially decreasing but eventually becomes increasing as

x

grows? (a)

(-2,2)

(b)

(0,2)

(c)

(1,2)

(d)

(-2,-2)