## AP Calculus AB Questions

1. Find  . (5 points)

 ·         5x2 + h2 + 7 ·         10x ·         3x2 – 2 ·         10x – 2

2. Given  find f ‘(x) and give its domain. (5 points)

 ·          Domain: All real numbers, x ≠ 2, 4. ·          Domain: All real numbers. ·          Domain: All real numbers, x ≠ 2. ·          Domain: All real numbers, x ≠ 4.

3. Use a graphing calculator to graph  and then select the response which is true. (5 points)

 ·         f increases without bound ·         f has no tangent line ·         f has a horizontal tangent line ·         none of these responses

4. Find  for y = 3cos(x) + sec(x). (5 points)

 ·         -3sin(x) + sec(x)tan(x) ·         3cos(x) – sec(x)tan(x) ·         3sin(x) – sec2(x) ·         3cos(x) – sec(x)

5. Differentiate  . (5 points)

 ·         -1 ·         -2csc(x) ·         2csc(x) ·

6. Which one of the following statements is true? (5 points)

 ·         If f and g are differentiable, then  . · ·         If f and g are differentiable, then  . ·         None of these statements are true.

7. Is the following true or false?

(5 points)

 ·         True ·         False

8. FREE RESPONSE If h(x) = f[g(x)], use the table of values for f, g, f ‘ and g ‘ to find the value of h ‘(1). (5 points)

 x f(x) g(x) f ‘(x) g ‘(x) 1 3 2 2 6 2 1 8 5 7 3 7 2 7 9

#8 (answer)___________________________

9. Determine the slope of the graph of x4 = ln(xy) at the point (1, e). (5 points)
 ·         3e ·         e4 ·         1 ·         4

10. Find y’ if x = sin(x + y). (5 points)

 · ·         1 ·         0 ·         cos(x + y)
11. Use the graph of f(x) below to estimate the value of f ‘(3):

(4 points)

 ·         -5 ·         -1 ·         0 ·         1

12. Given the graph of f ‘(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? (4 points)

I.The graph of f is decreasing on the interval (0, 2).
II.The graph of f is increasing on the interval (1, infinity).
III.The graph of f has point of inflection at x = 0.

 ·         I only ·         II only ·         III only ·         None of these are true

13. Find the critical point of the function f(x) = x2 – 2x + 7. (4 points)

 ·         (-1, 10) ·         (-1, 6) ·         (1, 0) ·         (1, 6)

14. For what values of x is the graph of  concave upward? (4 points)

 ·         No values of x ·         x < 6 ·         x > -6 ·         x > 6

15. At what value(s) of x does f(x) = x4 – 18x2 have a critical point where the graph changes from decreasing to increasing? (4 points)

 ·         0 and -3 only ·         0 and 3 only ·         -3, and 3 only ·         0 only

16. The maximum value of f(x) = 2x3 – 18x2 + 48x – 1 on the interval [0, 3] is (4 points)

 ·         -1 ·         39 ·         35 ·         71

17. In which interval is the function f(x) =  – 4x2 + 12x + 1 increasing? (4 points)

 ·         (-∞, 2) only ·         (-∞, 2) U (6, ∞) ·         (6, ∞) only ·         (2, 6) only

18. What are the critical values on the graph of y = x3 – 12x + 1? (4 points)

 ·         x = -2, 0, 2 ·         x = -2, 2 ·         x = -4, 4 ·         x = -3.42, 0, 3.42

19. Find the x-coordinate of the point(s) of inflection on the graph of y = x3 – 12x2 – 5. (4 points)

 ·         x = -2 ·         x = 4 ·         x = 2 ·         x = 12

20. Which one of the following statements is true? (4 points)

 ·         If f “(x) > 0 on the interval (a, b) then f(x) is concave down on the interval (a, b). ·         If f ‘(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b). ·         If f ‘(c) = 0, then x = c is a relative maximum on the graph of f(x). ·         None of these are true.