AP Calculus AB Theorems and Definitions

Quiz yourself on definitions and theorems for AP Calculus AB

1. AP Calculus AB Definition and Theorems BINGO

2. We say the ______ exists if:

3. We say the limit exists if:

4. if f is continuous on [ a, b ] , then there are x 1 , x 2 such that and What theorem is this?

5. if f is continuous on [ a, b ] , then there are x 1 , x 2 such that and Extreme Value Theorem

6. _________ occurs at x = a if

7. A removable discontinuity occurs at x = a if

8. Suppose g ( f ( x )) = x and f is differentiable. If What theorem is this?

9. Suppose g ( f ( x )) = x and f is differentiable. If Inverse Function Theorem

10. g is the _________ of f is defined if

11. g is the inverse of f is defined if

12. the _________ of f on [ a, b ] is defined to be

13. the average rate of change of f on [ a, b ] is defined to be

14. the _________ of f on [ a, b ] is defined to be

15. the average value of f on [ a, b ] is defined to be

16. A function is ______ if:

17. A function is continuous if:

18. A function is ______ if:

19. A function is increasing if:

20. A function is ______ if:

21. A function is decreasing if:

22. A function is ______ if:

23. A function is concave down if:

24. if f is continuous on [ a, b ] there is a What theorem is this?

25. if f is continuous on [ a, b ] there is a Mean Value Theorem for Integrals

26. _________ occurs at x = a if

27. A nonremovable discontinuity occurs at x = a if

28. if a function f is continuous and Theorem What theorem is this?

29. if a function f is continuous and Fundamental Theorem of Calculus I

30. _________ is defined to be

31. The derivative of f is defined to be

32. _________ occurs at a point at which

33. An inflection point of f occurs at a point at which

34. _________ occurs at a point at which

35. A critical point of f occurs at a point at which

36. ________occurs at a point at which

37. A relative max of f occurs at a point at which

38. _________ occurs at a point at which

39. A relative minimum of f occurs at a point at which

40. _________ to f at x = a has an equation

41. A tangent line to f at x = a has an equation

42. if a function f is continuous Theorem What theorem is this?

43. if a function f is continuous Theorem The Fundamental Theorem of Calculus II

44. an _____________ of f is a function F such that

45. an antiderivative of f is a function F such that

46. the _____________ is defined to be

47. the integral of f from a to b is defined to be

48. if f is continuous on [ a, b ] and differentiable on ( a, b ) there is a What theorem is this?

49. if f is continuous on [ a, b ] and differentiable on ( a, b ) there is a The Mean Value Theorem for Derivatives

50. if f is continuous on [ a, b ] , for every M between Theorem What theorem is this?

51. if f is continuous on [ a, b ] , for every M between Theorem Intermediate Value Theorem

52. A function is ______ if:

53. A function is concave up if:

54. _________ occurs at x = a where a is

55. A vertical asymptote occurs at x = a where a is

56. _________ occurs if is not + or - infinity

57. A horizontal asymptote occurs if is not + or - infinity