A lesson for when we can't get to school

1. Introduction to Slope Fields E. Alexander Burt Potomac School Something to keep you busy on your impromptu February break!

4. As you can see, this equation is the derivative of y=x 3 – OR IS IT?!

6. But it's also the derivative of y=x 3 +5 and y=x 3 -2 and y=x 3 + p .

10. The derivative gives us the slope of the tangent line.

12. “trust content” if necessary to get the applet to run.

14. Hopefully you'll get a set of lines that look like maybe you could put a y=x 3 +C curve in there.

15. It should look like this

17. dy/dx = 3x 2

18. y=x 3 +C is the solution

19. If we knew one point, we could find a specific solution – in other words, we could find C

21. You can also enter the point in the “add init cond” boxes – try it!

22. Slope Field with One Curve

24. Solving: dy/dx = -x/y

26. Try it with Min. x set to -6.28 and Max x set to 6.28

27. Click in a few places to see tan (x) + C