GoConqr has a new look! Let us know what you think.

Sign up free

Flashcards

AP Exam Definitions and Theorems and Examples

Brendan Kinnell English 39 cards

The average value of f(x) on [a, b] is...

Cards in this deck (39)

  1. 1The average value of f(x) on [a, b] is...The average value of f(x) on [a, b] is...
  2. 2The average Rate of Change of f(x) on [a, b] is...The average Rate of Change of f(x) on [a, b] is...
  3. 3f(x) is continuous at x = cf(x) is continuous at x = c
  4. 4f(x) is differentiable at x = cf is continuous at x = c
    AND    f(x) is differentiable at x = c
  5. 5If f(x) is continuous on (a, b) and differentiable on [a, b] then there is at least one value c in (a,b) where f'(c) =If f(x) is continuous on (a, b) and differentiable on [a, b] then there is at least one value c in (a,b) where f'(c) =
  6. 6—
  7. 7The absolute minimum (or maximum) of a continuous function f(x) on [a, b] must occur...At the endpoints of [a, b], (i.e. x = a, x = b) or at a critical point of f(x) on (a, b)
  8. 8If f(x) is continuous on [a, b] then there is a value c in (a, b) such that f(c) = k, where k is...any value for which f(a) ≤ k ≤ f(b)
    (Intermediate Value Theorem)
  9. 9f(x) has a point of inflection at x = c if...f has a tangent line at x = c
    AND
    f''(x) changes sign
    OR
    f'(x) changes from increasing to decreasing (or vice versa)
  10. 10—11
  11. 11The displacement (change in position) of a particle moving along the x-axis between t = a and t = b isfinal position - initial position
    OR
    x(b) - x(a)
    OR    The displacement (change in position) of a particle moving along the x-axis between t = a and t = b is
  12. 12The total distance traveled by a particle moving along the x-axis between t = a and t = b isThe total distance traveled by a particle moving along the x-axis between t = a and t = b is
  13. 13when a particle moves along a straight line, one relationship between initial position, final position, and velocity is...where x(t) is the position at time t
    and v(t) is the velocity at time t    when a particle moves along a straight line, one relationship between initial position, final position, and velocity is...
  14. 14If x(t) is the position of a particle along a number line at time t, then x'(t) represents...the velocity of the particle at time t,
    v(t)
  15. 15—f'(x)f'(x)
  16. 16—f'(3)f'(3)
  17. 17If f(x) = g(h(x)), then f'(x) =g'(h(x)) h'(x)
  18. 18If k'(x) > 0, then...k(x) is increasing
  19. 19if k'(x) < 0, thenk(x) is decreasing
  20. 20If the area and radius are related as shown above, then the relationship of the rate of change of A to the rate of change of r is...**you don't have to memorize this...
    just know that implicit differentiation is the technique to relate rates of change!    If the area and radius are related as shown above, then the relationship of the rate of change of A to the rate of change of r is...If the area and radius are related as shown above, then the relationship of the rate of change of A to the rate of change of r is...
  21. 21If g''(x) > 0, theng'(x) is increasing
    AND
    g(x) is concave upward
  22. 22if g''(x) < 0, theng'(x) is decreasing
    AND
    g(x) is concave downward
  23. 23if h'(x) is increasing, thenh(x) is concave upward
    AND
    h''(x) > 0
  24. 24If h'(x) is decreasing, thenh(x) is concave downward
    AND
    h''(x) < 0
  25. 25If L(t) is increasing, thenL'(t) > 0
  26. 26If L(t) is decreasing, thenL'(t) < 0
  27. 27If R(x) > 0 on the interval [a, b], then the graph of R(x) is...above the x-axis on [a, b]
  28. 28If f(x) is continuous and f'(x) > 0 on the interval -3 < x < 2 and f'(x) < 0 on the interval 2 < x < 5, thenf(x) has relative maximum at x=2
  29. 29If g(x) is continuous and if g(x) has a relative minimum at x = -2, then...g'(x) < 0 on the interval left of x = -2 and g'(x) > 0 on the interval right of x = -2
    OR
    g'(-2) = 0 and g''(-2) > 0
    (g has a horizontal tangent line at x = -2 and is concave upward at x = -2)
  30. 30A particle moving along a line with velocity v(t) is speeding up if...v(t) > 0 AND v'(t) > 0
    OR
    v(t) < 0 AND v'(t) < 0
  31. 31If V is related to r and h as shown above, then the relationship of the rate of change of V to the rate of change of r and the rate of change of h is...**you don't have to memorize this...
    just know that implicit differentiation is the technique to relate rates of change!    If V is related to r and h as shown above, then the relationship of the rate of change of V to the rate of change of r and the rate of ch...If V is related to r and h as shown above, then the relationship of the rate of change of V to the rate of change of r and the rate of ch...
  32. 32—
  33. 33—
  34. 34Using L'Hopital's Rule,Using L'Hopital's Rule,Using L'Hopital's Rule,
  35. 35If f is the inverse of g, and f(a) = b, then g'(b) =If f is the inverse of g, and f(a) = b, then g'(b) =
  36. 36A solid whose cross sections each have an area of A(x) for x-values between x = a and x = b has a volume that can be computed by...A solid whose cross sections each have an area of A(x) for x-values between x = a and x = b has a volume that can be computed by...
  37. 37Four ways to compute the value of a integral are...1. Find and evaluate an antiderivative
    2. Use geometry/area if given the graph
    3. Evaluate the integral on your calculator
    4. Estimate the integral using LRAM, RRAM, MRAM, or the Trapezoidal Method
  38. 38—f'(4)f'(4)
  39. 39L(t) measures how many people are waiting in line t hours after noon, then L'(3) = 7 can be interpreted how?L'(3) = 7 people/hr
    At 3pm, the number of people in line is INCREASING by 7 people per hour.

Information

Description
Flashcards on AP Exam Definitions and Theorems and Examples, created by Brendan Kinnell on 25/04/2018.
Created by
Brendan Kinnell
Views
10
Rating

Feedback

What is it about?

What do you think of the new look?

How do you like it?