Final Exam Problems(Please extend sufficient space if you work on the docx version)[10 points]1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function:[20...

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Final Exam Problems (Please extend sufficient space if you work on the docx version) [10 points] 1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function: [20 points] 2. Let , where is the function whose graph is shown below. a) Evaluate , , , , and b) On what intervals is increasing? c) Where does have a maximum value? d) Sketch a graph of the function [25 points] 3. Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral. a) b) c) d) e) [10 points] 4. Find the indefinite integral: a) b) [10 points] 5. Find the area of the region bounded by the curves: and [10 points] 6. Find the average value of the function on the interval [9 points] 7. A tennis ball is thrown vertically downward from a height of 54 feet with an initial velocity of 8 feet/sec. a) What is the velocity of the ball at time ? b) What is the position of the ball at time ? c) What is the impact velocity if it hits a 6-foot tall person on the head? [6 points] 8. The fuel tank on a large truck has trapezoidal cross sections with dimensions (in feet) shown in the figure below. Assume that the engine is approximately 2 feet above the top of the fuel tank and that diesel fuel weighs approximately 55.6 pounds per cubic foot. Find the work done by the fuel pump in raising a full tank of fuel to the level of the engine. Hint: Use the fact that