# 3 4 pts use the linearization in problem 2 to

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(3) [4 pts] Use the linearization in problem 2 to estimate sin( π - 1 10 ) (4) Note that you are not asked to determine where the function is concave up/down nor do you need to find the points of inflec- tion. Be careful when computing f 0 ( x ) ! Given the function y = f ( x ) = ( x +2) 2 x 2 - 1 (a) [2 pts] Find the x and y intercepts of the function. (b) [2 points] Find all asymptotes.

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(c) [2 pts] Find the open intervals where f ( x ) is increasing and the open intervals where f ( x ) is decreasing. (d) [2 pts] Find the local maximum and local minimum values of f ( x ). (Be sure to give the x and y coordinates of each of them). (e) [5 pts] Use the above information to graph the function below. Indicate all relevant information in the graph; in particular any absolute/local maxima/minima .
(5) [9 pts] If y = f ( x ) = 3 x 2 - 1, find the absolute maximum and minimum of f ( x ) on the closed interval [ - 2 , 2]. (Include the appropriate y values, simplify when possible.)

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(6) [10 pts] A cannon tracks an air plane which flies at a constant altitude of 5 km and a speed of 300 km/h directly toward the cannon. How fast (in radians/hour) is the angle between the cannon and a vertical line decreasing when the plane is 5 km away from the point P straight above the gun which is at an altitude of 5 km. 5 km Cannon Plane P θ
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