1. Calculus Section 4.2 Find 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
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6. Assignment
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Problems 2 – 40 even, 44,45