AP Calculus Review

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3. Find equation of the line normal to on

4. Show that is even

5. Show that is odd

6. Find the interval where is increasing

7. Find interval where the slope of is increasing

8. Find the minimum value of a function
9. Find the minimum slope of a function
10. Find critical values
11. Find inflection points
12. Show that exists

13. Show that is continuous

14. Find vertical asymptotes of

15. Find horizontal asymptotes of

16. Find the average rate of change of on

17. Find instantaneous rate of change of at a

18. Find the average value of on

19. Find the absolute maximum of on

20. Show that a piecewise function is differentiable
at the point a where the function rule splits
21. Given (position function), find

22. Given , find how far a particle travels on

23. Find the average velocity of a particle on

24. Given , determine if a particle is speeding up
at

25. Given and , find

26. Show that Rolle’s Theorem holds on

27. Show that Mean Value Theorem holds on

28. Find domain of

29. Find range of on

30. Find range of on

31. Find by definition

32. Find derivative of inverse to at

33. is increasing proportionally to

34. Find the line that divides the area under
on to two equal areas

35.

36.

37. The rate of change of population is …
38. The line is tangent to at

39. Find area using left Reimann sums
40. Find area using right Reimann sums
41. Find area using midpoint rectangles
42. Find area using trapezoids
43. Solve the differential equation …
44. Meaning of

45. Given a base, cross sections perpendicular to the
x-axis are squares
46. Find where the tangent line to is horizontal

47. Find where the tangent line to is vertical

48. Find the minimum acceleration given

49. Approximate the value of by using the
tangent line to f at

50. Given the value of and the fact that the anti-
derivative of f is F, find 1

51. Find the derivative of

52. Given , find

53. Given a picture of , find where is
increasing
54. Given and , find the greatest distance
from the origin of a particle on

55. Given a water tank with g gallons initially being
filled at the rate of gallons/min and emptied
at the rate of gallons/min on , find
a) the amount of water in the tank at m minutes

56. b) the rate the water amount is changing at m

57. c) the time when the water is at a minimum
58. Given a chart of x and on selected values
between a and b, estimate where c is
between a and b.
59. Given , draw a slope field

60. Find the area between curves on

61. Find the volume if the area between is
rotated about the x-axis