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1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the distance 5 between the airplane and the radar station is decreasing at a rate of 400 km per hour when 3:10 km., what is the horizontal speed of the plane? Make sure your answer includes units. 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the deck, positioned 6 meters higher than the boat. If the rope is being pulled in at a rate of 3 meters/sec, how fast is the boat approaching the dock when it is 8 meters from the dock? Make sure your answer includes units. 3. A girl is flying a kite on a string. The kite is 120 ft. above the ground and the wind is blowing the kite horizontally away from her at 6 ft/sec. At what rate must she let out the string when 130 ft of string has been released? Make sure your answer includes units. 4. Find the Linearization of f(1:) = sing: at a = 31. Provide your answer as L(1:) =? 5. Use Linear Approximation to estimate e(0-01). Provide your answer in 2 decimal places. Do not use a calculator. Show work for credit. 6. Calculate the locations of maximums and minimums of the following functions: Show work in details. ' f(3:)=3:33:1:+2 f(a:)=:v48:1:2-+-3 7. Find the exact x-value where the function f(:r:) = :1: + In (332 _ 1) attains a maximum value. An estimated answer or a calculator answer will not earn any credit. 8. Using the Mean Value Theorem and Rolle's Theorem, show that/:3 + 1; _ 1 = 0 has exactly one real root. 9. lff(1) = 10 and f'(1:) Z 2for1 S g; g 4, how small canf(4) possibly be? 10. The graph of a function is given below. Determine the intervals on which the function is concave up and concave down