Methods of Calculus, MAC3233 Final Exam April 28, 1993 Instructions: Do not write your answers on this paper, use separate answer sheets. This is a closed-book test. No calculators are allowed to be used. Time limit: 2.75 hours. (1) (10 points) Diﬀerentiate: f ( x ) = 4(9 x 7 + 2 x-5)-3 (2) (15 points) Find the equation of the tangent line to the graph of f ( x ) = 3 + 2 x 2 at x = 1. (3) (20 points) For the function f ( x ) =-1 3 x 3 + 3 x 2-5 x (a) Give f0 ( x ) and f 00 ( x ). (b) Find all local extrema and classify each as a relative maximum or minimum. (c) Find all inﬂection points. (d) Sketch the graph. (4) (20 points) Someone wants to build a 600-square-foot rectangular enclosure. Three sides of the enclosure will be built of redwood fencing, at a cost of $8 per running foot. The fourth side will be built of cinder blocks, at a cost of $16 per running foot. Find the dimensions of the rectangular enclosure that will minimize the total cost of the building materials. (a) Give the objective function.
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