Mathematics

Problem

A student plans to sketch the slope field for

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

on the

3\times3

lattice consisting of all points

(x,y)

where

x

and

y

are integers and

-1\le x\le1

-1\le y\le1

. At how many of these nine lattice points will the slope of the short segment satisfy

0\le m<1

? a) 6 b) 3 c) 2 d) 4