f(x) = if x * 2 x - 2 if x = 2 6. Let f be the function defined above. Which of the following statements about f are true? I. f has a limit at x = 2. II. f is continuous at x = 2. III. f is differentiable at x = 2. (A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III 7 . A particle moves along the x-axis with velocity given by v(1) = 3t2 + 6t for time 1 2 0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at time t = 1? (A) 4 (B) 6 (C) 9 (D) 11 (E) 12 8. If f(x) = cos(3x), then f' ( A) 3V3 2 (B) V3 (C) V3 2 (D) N / W (E) 3V/3 2 2 9 . If f ( x) = ex, then f' (x) = ( A ) 2e s Inx (B) e(3 x ) (C) e(7/ x2 ) (D). 2 (3) x 2 (E) - 2x2 @(3/x) 10 . If f(x) = x2 +2x, then (f(Inx))=( (A) 2 In x + 2 (B) 2xIn+ 2x (C) 2Inx+2 (D) 2Inx+2 2x + 2 X ( E - X 1 1 . Let fbe a function with a second derivative given by f"(x) = x2(x-3)(x -6). What are the x-coordinates of the points of inflection of the graph of f? (A) 0 only (B) 3 only (C) 0 and 6 only (D) 3 and 6 only (E) 0, 3, and 6