Calculus Section 4.2 Find relative extrema and graph functions

1. Calculus Section 4.2Find relative extrema and graph functions Recall: the derivative of a function can be used to determine when the graph is increasing and decreasing The slope of a graph is positive to the left of a relative maximum and negative to its right. The slope of a graph is negative to the left of a relative minimum and positive to it right.

2. First Derivative Test – is used to determine whether a critical point is a relative maximum or minimum 1st Derivative Test If c is a critical number on f(x); • If f’(x) > 0 left of c and f’(x) < 0 right of c, then (c,f(c))is a relative maximum. • If f’(x) < 0 left of c and f’(x) > 0 right of c, then (c,f(c))is a relative minimum.

3. Find the relative extrema (relative max/min) f(x) = x3 – 3x2 + 1 To find the relative extrema • Find the derivative • Find the critical points • Make a sign graph using the derivative • Determine max/min by 1st derivative test

4. Find the relative extrema and graph the function f(x) = -x3 + 3x + 5 f(x) = x2/3 + 1

5. Find the relative extrema F(x) = x3 + 2 Page 203 ex 4

6. Assignment • Page 204 • Problems 2 – 40 even, 44,45