AP Calculus Chapter 3

  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
Card Set
AP Calculus Chapter 3
These are my flashcards for the third chapter of my book, Calculus of a single variable AP edition