The First Derivative Test

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Presentation transcript:

The First Derivative Test Section 3.3 The First Derivative Test

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.

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

Homework p. 186 # 3-7 odd, 17-37 EOO, 43, 45, 59-63 odd, 89, 91