Calc

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Author:
jeffcindric
ID:
115802
Filename:
Calc
Updated:
2011-11-09 20:44:18
Tags:
Calc AP AB
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Description:
Chapter 3
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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.

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