# Calc

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1. Extrema
The maximum and minimum value of an interval.
2. Extreme Value Theorm
If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.
3. Relative extrema
The highest or lowest point on a "hill".
4. Critical numbers
A point at which f'(x) equals 0 or is undefined.
5. How to find extrema on a closed interval:
• 1. Find critical numbers.
• 2. Evaluate f at each critical number in the interval.
• 3. Evaluate each endpoint of the interval (if it's closed)
• 4. The least is the minimum. The greatest is the maximum.
6. Rolle's Theorem
If f is continuous on the closed interval and differentiable on the open interval and if the endpoints have the same y value, there is at least one number c in the interval such that f'(c) = 0.
7. Mean Value Theorm
If f is continuous on the closed interval and differentiable on the open interval, then there is a tangent line whose slope is the same as the slope between the two endpoints (or the secant line).
8. Increasing and Decreasing Functions
• 1. If f'(x) > 0 for all x in an interval, then f is increasing on that interval.
• 2. If f'(x) < 0 for all x in an interval, then f is decreasing on that interval.
• 3. If f'(x) = 0 for all x in an interval, then f is constant on that interval.
9. First Derivative Test
If f'(x) changes from neg/pos to pos/neg at c, the there is a relative max or min at c.

### Card Set Information

 Author: jeffcindric ID: 115802 Filename: Calc Updated: 2011-11-10 01:44:18 Tags: Calc AP AB Folders: Description: Chapter 3 Show Answers:

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