2014 AP CALCULUS AB FRQs

1. 2014 AP CALCULUS AB FRQs

3. Average rate of change = lbs/day

4. On the fifteenth day the amount of grass clippings is decreasing at the rate of 0.1635 lbs/day

5. Average amount of clippings: Solvedays

6. Tangent line at is Solve days

8. y= 4 f(x) Intersections of the two graphs: and

9. y= 4 f(x) Length of the rectangle: y – f(x)

10. y= 4 f(x)

11. y= 4 f(x)

12. y= 4 f(x)

15. , therefore if g(x) increases . This happens on the intervals and (−3, 2) If g(x) i decreases. This happens on and (0, 4) g(x)is increasing and concave down on and (0, 2)

17. The slope of the graph of f at is −2, so

19. Average acceleration of train A: S meters/minute2

20. Since is differentiable, it is also continuous so the Intermediate Value Theorem applies to for . Therefore, there must be at least a value such that meters/minute

21. meters

22. Train B meters meters meters z = distance between the two trains y Train A x At minutes,

24. f has a local minimum when its derivative, f’, switches from negative to positive. This occurs at x = 1.

25. f is twice differentiable so its derivative, f’, is both continuous and differentiable. Therefore the Mean Value Theorem can be used on f’ . There must be a value for such that Since

26. The problem can also be done using Rolle’s Theorem: f is twice differentiable so its derivative, f’, is both continuous and differentiable. And since Rolle’s Theorem can be used on f’. Therefore, there must be a value for such that

31. Equation of the tangent line:

32. Using (0, 1):