5 To apply either the Mean Value Theorem Rolle's Theorem to a function f, certain requirements regarding the continuity and differentiability of the function must be met. Which of the following states the requirements correctly? (A) fis continuous on (a, b) and differentiable on (a, b) (B) / is continuous on (a, b) and differentiable on [a, b] (C) fis continuous on (a, b) and differentiable on [a, b) (D) / is continuous on [a, b] and differentiable on (a, b) (E) f is continuous on [a. b] and differentiable on [a, b] 6. If the length of a rectangle is increasing at the rate of 7 cm/sec and the width of the rectangle is decreasing at the rate of 7 cm/sec, then which of the following best describes the change in area when the length is greater than the width? (A) none (it remains constant) (B) always increasing (C) always decreasing (D) decreasing then increasing (E) increasing then decreasing 7. A ball is thrown from the top of a 1200-foot building. The position function expressing the height h of the ball above the ground at any time / is given as h(x) = -161 -101 + 1200. Find the average velocity for the first 6 seconds of travel. (A) - 202 fusec (B) - 106 fu/sec (C) -86 fusec (D) - 74 fu/ sec (E) 74 fu/sec 8. The area of an equilateral triangle can be expressed in terms of a side s as A = If the area is 4 increasing at five times the rate that the sides are increasing, what is the perimeter of the triangle? (A) 3 (B) 8V3 8V/3 (D) 10 V3 (E) 10V3 5 3 3 9 Over which interval is the function f(x) = 3x - 20x -12 increasing? (A) (-20, -2) only (B) (-0,2) only (C) (-on,-2) and (2, 30) (D) (-2,2) (E) (- 2,0) and (0,2)