Mathematics

Problem

Which quantity do the short line segments in a slope field directly represent for the differential equation

\dfrac{dy}{dx}=f(x,y)

? a) the

y

-value at the point b) the curvature

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

at the point c) the derivative

\dfrac{dy}{dx}

at the point d) the approximate change

\Delta y

for a unit change in

x

at the point