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209-2-sample(2)

# 209-2-sample(2) - tions require you to keep the price above...

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DEPARTMENT OF MATHEMATICS AND STATISTICS MATH 209 Second class test duration 1h20m 1. [15pts] Find dy dx of the following (a) y = ( x 2 + 4 x ) 5 ( x 5 + 2) 3 , (b) y = [ x 2 + ln( x - 2)] 3 , (c) y = ln x e x +1 . 2. [30pts] For the function f ( x ) = x +1 x 2 (a) locate horizontal and vertical asymptotes and x - and y -intercepts (if any) (b) ﬁnd critical points, intervals of increasing/decreasing and local max- ima/minima (c) ﬁnd inﬂection points and determine where f ( x ) is concave up/down (d) ﬁnd values of f ( x ) at the critical and inﬂection points and sketch the graph of the function. 3. [20pts] The price-demand equation for the new plasma TV is x = 10 , 000 - 10 p . The cost of the production is C ( x ) = 500 , 000 + 300 x . Anti-dumping regula-
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Unformatted text preview: tions require you to keep the price above \$600. (a) At which price you get the maximum revenue? (b) At which price you get the maximum proﬁt? 4. [10pts] Find horizontal asymptotes (if any) for the function y = e x e x + 1 . 5. [15pts] Having implicit relationship t 2 y 2-ty + t + y-2 = 0 ﬁnd dy dt at ( t,y ) = (1 , 1) and the equation of the line tangent to the graph at this point. 6. [15pts] The cost function is C ( x ) = 100 + x + 0 . 01 x 2 . Find C ( x ), C ( x ) , C ( x ) 00 , the minimum average cost and graph the function of the average cost....
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