Question

Slope fields?

Answer 1

This isn't a real question but how to tackle slope field questions. I'm in Calc BC and they covered it briefly last year in AB and I was hoping this year that they would be more in depth but it was the same overview. I was wondering if anyone had any

Characteristics of slope fields that are in one variable (e.g., y'y or y'x what would the lines look like in a general sense if it's just one variable) etc. any help or whatever you've picked up as patterns would be greatly appreciated!

Answer 2

@NoelGreco

Answer 3

Here's a great resource: http://tutorial.math.lamar.edu/Classes/DE/DirectionFields.aspx

Constructing a slope field isn't too difficult. It's a matter of selecting an appropriate domain of the \(x-y\) plane and plugging in these points to solve for the derivative at said point, given a first-order ODE \(y'=f(x,y)\).

Answer 4

If memory serves me (which I would take with a grain of salt, it's been nearly 4 years since), the AP tests didn't particularly cover material involving slope/direction fields, there were maybe 2 or 3 multiple choice questions given and one section of a multi-part free response about them.