MAT112 Test 3 Topics
- Increasing/Decreasing functions
- Definition on an open interval
- Critical numbers
- Relative Extrema
- If there is an extremum, then it will be found where the
derivative is zero, where the derivative doesn't exist, or at
the endpoints of intervals on which the function was defined.
- Use the first derivative to find critical
numbers, or critical points: where the derivative is zero or
undefined.
- Check the boundaries for additional possible extrema
- Use the first derivative test to decide if you have a max, a min,
or neither. (Don't forget that "neither" is also a
possibility!)
- Higher Derivatives
- second derivatives
- higher derivatives
- position/velocity/acceleration
- Remember that velocity also has direction
- Inflection points
- use the second derivative: where it's zero or undefined
- Second derivative test for extrema
- second derivative positive means concave up
- second derivative negative means concave down
- Curve sketching
- Study the "eight-fold way"
- Don't forget asymptotic behavior -- what's the function doing when
x gets really big or really negative?
- Don't forget to create a summary table.
- Absolute extrema and applications
- The biggest/smallest of the relative extrema
- Don't forget to check the boundaries!
- Don't forget your derivative rules!
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