Card Set Information
Calc AP AB
The maximum and minimum value of an interval.
Extreme Value Theorm
is continuous on a closed interval [
has both a minimum and a maximum on the interval.
The highest or lowest point on a "hill".
A point at which
'(x) equals 0 or is undefined.
How to find extrema on a closed interval:
1. Find critical numbers.
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.
is continuous on the closed interval and differentiable on the open interval and if the endpoints have the same
value, there is at least one number
in the interval such that
(c) = 0.
Mean Value Theorm
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).
Increasing and Decreasing Functions
'(x) > 0 for all
in an interval, then
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.
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.