# AP Calculus Chapter 3

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 Author: winterburger ID: 109670 Filename: AP Calculus Chapter 3 Updated: 2011-10-21 01:56:02 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:

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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
10. Concave Down
f ' x is decreasing, f '' x is negative, f (x) will shed water
11. Second Derivative ITSC
Find where the 2nd Derivative is 0 or undefined. Use those numbers to make intervals

• Intervals
• Test Value
• Sign of f '' x
• Conclusio
12. If f '' x is positive
interval is concave up
13. If f '' x is negative,
interval is concave down
14. Inflection Point
• Where the function is switching from concave up to concave down or
• from concave down to concave up.
15. 2nd Derivative Test
• 1. Plug your critical numbers into the 2nd Derivative
• 2. If the result is positive, then the there is a relative min at the critical
• number
• 3. If the result is negative, then there is a relative max at the critical
• number.
• 4. If the result is 0, the test fails
16. 0
17. (2/5)
18. Definition of a Differential
dy= f(x)dx
19. Definition of Δy
Δy= f(x+Δx) − f(x)
20. Optimization Problem
• 1. Write your two equations. The equation that you are minimizing or maximizing is the Primary Equation.
• 2. Get your Primary equation in terms of one variable by substituting in the other equation.
• 3. Differentiate your primary equation and find the critical numbers.
• 4. Show that the critical numbers are a max or min by the 2nd Derivative Test or a First Derivative ITSC