The slope field for has arrows that are horizontal along the parabola

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The slope field for

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

has arrows that are horizontal along the parabola

y=x^{2}

, point downward when

y>x^{2}

, and point upward when

y<x^{2}

. Choose one initial point

(x_{0},y_{0})

with

y_{0}>x_{0}^{2}

such that the corresponding solution curve will first decrease toward the parabola, reach a minimum on it, and then increase for all larger

x

. State your chosen point and briefly justify the predicted qualitative behavior.