1. An airplane is flying towards a radar station at a constant height of 6 km above the ground. If the distance s between the airplane and the radar station is decreasing at a rate of 400 km per hour when s=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(:v) 1 sinx at a = g Provide your answer as L(:c) =? 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(z)=za3.7:+2 'f(a:)=x48x2+3 7. Find the exact x-value where the function f(:1:) = as + ln (:52 _ 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 thatg;3 + :r _ 1 = 0 has exactly one real root. 9. If f(1) = 10 and f'(:c) Z 2for1 S :7: 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