1. The First Derivative Test
Section 3.3
The First Derivative Test

2. Things to remember: f(x) is increasing when f’(x) is positive
f(x) is decreasing when f’(x) is negative
At critical numbers, the slope of f(x) is 0.

4. The First Derivative Test
Helps us determine which points are local maximums and minimums
If f’(x) changes from negative to positive at c, then x = c is a relative minimum
If f’(x) changes from positive to negative at c, then x = c is a relative maximum
If f’(x) is positive on both sides of c or negative on both sides of c, then f(c) is an inflection point

7. Homework
p. 186 # 3-7 odd, EOO, 43, 45, odd, 89, 91