200

1. Are we related? What the ________ The Highs, The Lows Best Possible Category Upping The Anti 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500

2. Formula for surface area of a rectangular box that has a square base with side length x and height y

4. If Then when , and t = 1

5. ¾ or .75

6. If and find when x=4.

7. -8

8. A ladder 10 feet long rests against a vertical wall. If the ladder slides away from the all at a rate of 1ft/s, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 feet from the wall?

9. -3/4 ft/s(will accept ¾ ft/s if the direction is indicated)

10. A snowball melts at a rate of cubic inches per hour. What is the rate that the radius is changing when the snowball has diameter 6 inches? Volume of sphere

11. 1 in/hour

12. Extreme Value TheoremIf f is (1.)_______ on a (2.)______ interval, then f attains an absolute maximum and an absolute minimum on the interval.

13. (1.) continuous(2.) closed

14. Critical NumberA number c is a critical number of a function f(x) if f’(c) is either (1.)______ or (2.)______.

15. (1.) 0(2.) undefined

16. First Derivative Test If c is a critical number of a continuous function f, then: If f’ changes from + to – at x=c, then f(c) is a (1.)_______ If f’ changes from – to + at x=c, then f(c) is a (2.)________

17. (1.) local maximum(2.) local minimum

18. Second Derivative TestIf f’(c) = 0 and f”(c) > 0, then f has a (1.)________ at x=c. If f’(c) = 0 and f”(c) < 0, then f has a (2.)________ at x=c.

19. (1.) local minimum (2.) local maximum

20. Fundamental Theorem of Calculus, Part II Let f(x) be a continuous function on [a,b]. Then (1.)_____

21. (1.) f(x)

22. Find the local maximum(s)

23. Local max of 2 at x = 0.

24. Find interval(s) of where f(x) is increasing:

25. (-3, 0) U (3, ∞)

26. Find x-coordinate of any inflection points of g:

27. x = 1

28. Find the critical number(s) of On (-π/2, π/2)

29. x = 0

30. Suppose On what interval(s) is f decreasing?

31. interval (0, 1)

32. A box will be made by cutting out equal corners from four sides of a 12” by 26” piece of cardboard and folding up the sides. Write an expression for the volume of the resulting box (including the domain).

33. V(x) = x(12-2x)(26-2x)and [0,6] is the domain.

34. 5000 square inches of paper are to be used to make a poster with margins 2” on top and bottom and 3” on the sides. Draw a picture and write an expression (in one variable only) for the printed area of the poster.

35. May vary.

36. Find the absolute maximum and minimum of f(x) on the given interval

37. absolute maximum of 0 at x=0 and x=3absolute minimum of -1 at x=1

38. The problem is to find the right triangle of perimeter 10 whose area is as large as possible. What is the constraint equation relating the base b and the height h of the triangle?

40. What are the relevant variables if the problem is to find a right circular cone of surface area 20 and maximum volume?

41. radius r and height h

42. F(x) is an antiderivative of f(x) if (1.)________

43. F’(x)=f(x)

44. Find the general antiderivative:

46. Find s(t)if and s’(0)=1, s(0)=10

48. Daily Double

49. Evaluate