At the point a differential equation has a second derivative given by

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

At the point

(2,1)

a differential equation has a second derivative given by

y''=y^{2}-x

. If a single positive step of a tangent-line approximation is taken from

(2,1)

, indicate whether the numerical estimate of

y

at the next

x

-value will be above or below the actual solution value.