The graph above represents f # (x). Which of the following graphs represents f (2)? O O O8. The graph of f w(a) is shown below. If f na), fi(c), and fi(e) = 0 then at which point does f (x) have a local maximum? Graph of f" Od Oe O O O10. The graph of f (x) is shown below. On which of the following intervals is f /(x) both negative and increasing? A W -3 4 -3 -2 -1 0 1 2 3 O (0, 1) O (-1, 0) O (-20, -1) O (0, 60)3. The graphs of f /(x) and f #(2) are shown below. Which of the following statements best describes the equation of f (3)? Graph of f (x) WNHOPNW -3 Graph of f "(x) -3 -2 -1 0 2 A cosine function O A sine function A quadratic O A logarithmic function O A cubic 4. The graph of f (x) is shown below. Which statement best defines the graph of f /(x) at the point a = a? Graph of f O Zero O Undefined O Negative Positive 5. The graph of f #(a) is shown below. If fro), f "(c), and f (e) = 0 then at which point does f (a) have a local maximum? Graph of f" O O a6. The figure below shows the graph of f (x), f /(2), and fm(x) . Identify which graph corresponds with which line. .L.. -3 KEY 1 - Red 2 - Blue 3 - Green -4 -3 -2 1 2 3 4 5 1. f (2) 2. f 1(x) 3. f 1(2) 7. The graph of f /(x) is shown below. Which of the following accurately describes the graph of f (x) at point e? Graph of f' AY Inflection point Decreasing Increasing Critical point Concave up O Concave down1. The graph of f /(x) is shown below. Which of the following statements best describes the behavior of f (x) at point a? Graph of f" O Decreasing, concave up O Point of inflection, increasing O Decreasing, concave down O Increasing, concave down O Point of inflection, decreasing9. f (x) is a function with the following properties: f (x) has a local minimum at a = -1 f (2) is increasing on the interval (-1, 1) f (x) is decreasing on the interval (-co, -1) U (1, 00) Which of the following figures best depicts the graph of f /(:) ? 10 -10 -2 O NHOHNWA -3 -21. Considering the differential equation # = 7y + 3 with initial condition (0, 5), solve for y. Ov= -38e 72 + 3 Oy= -190 72 - 3 Oy= 14 14 40 Ou= Te* +41 Oy= 1807-3 2. If 42 - 24 - 2 =0, and y(0) = 7, then y = c' + 2: + 7. True O False 3. Solve the differential equation y/ = 8y, with y(0) = -4. Oy=ex -4 Oy= -82 - 4 Oy= -4In(8x) Oy= -4efax Oy= -5+32 4. The function y = Gelf - 10 solves the differential equation y/ - 6y = -5y -50. O False 5. Solve the differential equation @ = 7re", with the initial condition (0, 0). Ov=-72 Oy= - In(1 - 7x) Oy= In(2) - 14 In(x) Oy= - In(1 - 1:') Oy= -12 6. If f 1(x) = 4x - 2 and f (4) = 9, find f (x). Of (x) = 14 2 +9 Of (7) = 2:12 -2x+ -15 Of (x) = 4 In |42 - 2 + 9 Of (7) = 212+4 Of (7) = 36