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Unformatted text preview: Math 016A Name: ID Midterm 2 Signature Mar., 2009 Simplify your ﬁnal result if possible. No Calculators allowed. 1. (20pts)[a](8pt) Find the derivative of f (x) = [x2 (2x + 3)]3 . [b](12pt) Find the second derivative and solve the equation f (x) = 0 for f (x) = x x2 +1 2. (16pts) Find the equation of the tangent line to the graph of the following curve at point ( π , 1 ) : 22 √ sin x + 2 cos(xy ) = 1 + 2 1 3. (14pts) A boat is pulled by a winch on a dock and the winch is 8 feet above the deck of boat. The winch pulls the rope at the rate of 3f t/s. Find the speed of the boat when 10 feet of rope is out. What happens to the speed of the boat as it gets closer and closer to the dock? 4. (16pts)Find the critical numbers and open intervals on which the function f (x) = √ −3x 2x + 1 is increasing or decreasing. 2 5. (17pts)Find and identify all the local extrema of f (x) = x + 1 . x−1 6. (17pts)Find the global extrema of the function f (x) = 2 cos x − sin(2x) on the interval [0, 2π ]. Note that you may want to use trigonometric identities: sin(2θ) = 2 sin θ cos θ, or cos(2θ) = 2 cos2 θ − 1 = 1 − 2 sin2 θ. 3 ...
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 Spring '08
 DUANEKOUBA
 Calculus, Trigonometry, Derivative, Mathematical analysis, Continuous function, Convex function, Graph of a function

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