Sixthsense

Ok, so I was working on some multiple choice problems and free response questions that were dealing with slope fields. My first question is what exactly do you usually do when you are presented with a slope field and must pick the correct value of dy/dx.Do you select random points and pug them in and see if the y match or is there a more efficient method. Also, I was wondering on the free response how you differentiate between close slopes, like 3/2, and 2, when drawing a slope field.

Thanks

jamesford

Imo there are really only 4 types of slopes that can be clearly told apart from all the rest:

1
-1
0 (horizontal)
1/0 (vertical line)

So try to identify where one or more or those occurs, plug into (x,y) into dy/dx, and see if it matches.

For the free response, you can't really differentiate between 3/2 and 2. Just make sure you drew positive/negative slopes in the right direction (duh) and make sure that 5 is clearly steeper than 1.

intellec7

Also, they'll give you the points which you're supposed to place your slope lines on. I think it was 9 on the FRQ I saw.

Freezenthaw

my advice: go quadrant to quadrant. Start with the quadrants that are either...all positive or all negative. Then do process of elimination. This works well (obviously for MC only). Usually you can eliminate 3/5 answer choices just by analyzing a quadrant for a consistent slope.

somni

That's not true. Sometimes they want to be able to see a d(dy/dx)/dy, so make them look different if they're supposed to