5 y 5x 42x 3 x 2 1 a 10x 3 13x 2 39x 5 b 40x 3 13x 2

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5) y = (5x - 4)(2x 3 - x 2 + A) 10x 3 + 13x 2 - 39x + 5 B) 40x 3 - 13x 2 + 39x + C) 30x 3 + 39x 2 - 13x + 5 D) 40x 3 - 39x 2 + 8x + 1) 5 5 SHORT ANSWER. You must show all your work to receive full credit. Use implicit differentiation to find dy/dx and d 2 y/dx 2 . 6) xy - x + y = 5 Use analytic methods to find those values of x for which the given function is increasing and those values of x for which it is decreasing. 7) f(x) = 2x 2 + 4x Solve the problem. 8) A spherical balloon is inflated with helium at a rate of 110 Δ ft 3 /min. How fast is the balloon's radius increasing when the radius is 4 ft? 9) The position s (in miles) of a particle is modeled by the following function of time t (in hours): Find the velocity and acceleration functions with respect to time. What is the velocity of this object at time t = 45 minutes? What is the acceleration of this object at time t = 45 minutes? Graph the position, velocity, and acceleration functions on the interval [0, 6]. Pinpoint when the object is moving forward and when it is moving backward. Give the time intervals in which the object is speeding up. Give the time intervals in which the object is slowing down. 2
Use the graph of f to estimate where f'' is 0, positive, and negative. 10) BONUS PROBLEM (5 points) 3

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