Here are some handy characteristics to start with -- you will develop more as you practice.

A.Sety equal to zero and look at how the derivative behaves along thex -axis.

B.Do the same for they -axis by settingx equal to0

C.Consider the curve in the plane defined by settingy'=0 -- this should correspond to the points in the picture where the slope is zero.

D.Settingy' equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and can be used to construct the direction field picture by hand.

**1.** **2.** **3.** **4.**

A | B |
---|

C | D |
---|