Mathematics

Problem

The differential equation

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

defines a slope field. For the solution curve that passes through

(1,1)

, which statement best describes the concavity of the solution at that point? a) Concave upward because

\dfrac{d^{2}y}{dx^{2}}=1>0

(1,1)

.},{ b) Point of inflection because

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

(1,1)

.},{ c) Concave downward because

\dfrac{d^{2}y}{dx^{2}}=-1<0

(1,1)

.},{ d) Cannot be determined without explicitly solving for

y(x)

.}],