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Unformatted text preview: x a ) f ( a ) dy . 2. 3. 4. Absolute Maximums and Minimums: Extreme Value Theorem: Continuous functions on a closed interval will have an absolute max and min. To find absolute maxs and mins, take the derivative, and find the x‐values where the derivative is 0 or undefined. These are the critical points. Test the critical and the endpoints of the interval in the original function. The largest value is the absolute max and the smallest value is the absolute min. Local Maximums and Minimums: Local maxs and mins can only occur at critical points where the original function is defined. a. First Derivative Test If c is a critical values where the original function is defined, create a sign chart and test a nearby point on both in the first derivative to see if it are positive or negative. If the sign is the same on both sides of c, it is not a local max or min. b. Second Derivative Test If c is a critical values where the original function is defined, plug c into the second derivative. If the second derivative is negative, you...
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This note was uploaded on 02/24/2014 for the course MATH 1151 taught by Professor Daniel during the Fall '12 term at Ohio State.
- Fall '12