# AP Calculus Chapter 3

The flashcards below were created by user Anonymous on FreezingBlue Flashcards.

1. Critical Numbers
Values of x in the domain of f (x) where f 'x= 0 or f 'x is undefined
2. How do you find absolute minimums and maximums on a closed interval?
• 1. Find critical numbers
• 2. Find values for the function at each endpoint and critical number
• 3. Determine absolute max and absolute min for the interval by your results from step 2.
3. Rolle’s Theorem
• If f is differentiable on the interval (a , b) and f(a) = f(b) then there is at least one place in the interval
• where f 'x= 0
4. Mean Value Theorem (MVT)
• If f (x) is continuous and differentiable on the interval [a , b], there is someplace in the interval where f ' x
• equals the slope of the line going through the endpoints of the interval.
5. First Derivative ITSC
1) Use critical numbers to determine intervals.

• Interval
• Test Value
• Sign of f ' x
• Conclusion
6. If sign of f ' x is positive what is happening to f(x)?
f(x) is increasing
7. If sign of f ' x is negative then f(x) is _______.
f(x) is decreasing
8. First Derivative Test
Do a first derivative ITSC,

• If f ' x is changing from pos to neg, then relative max
• If f ' x is changing from neg to pos, then relative min
9. Concave Up
f'(x) is increasing, f''(x)is positive, f(x) will hold water
 Author: Anonymous ID: 109669 Card Set: AP Calculus Chapter 3 Updated: 2011-10-17 21:45:01 Tags: AP Calculus BC Chapter Folders: Description: These are my flashcards for the third chapter of my book, Calculus of a single variable AP edition Show Answers: