The 1st Derivative Test

The 1st Derivative Test is simple way to prove that critical points are extrema (or are not extrema in some cases).  Make sure you do the following:

1. Find critical points
2. Test points on both sides (using the 1st derivative)
3. Compare the slopes (+ or -)...if it goes - to +, it's a min..if it goes + to -, it's a max.  If it doesn't change...then it's NOT an extrema!

Don't forget to include the increasing and decreasing intervals on your HW.  Use your graphing calculator to help with this.  

Curve sketching is a little trickier.  The following will be helpful:

• f(3) = 4 means graph the point (3,4)
• f'(x) = 0 means you have a max or min
• f'(x) DNE means you have a cusp, corner, or asymptote
• f'(x) >0 means increasing and f'(x)<0 means decreasing

See video for problem #11 and #36.