03_Midterm2-Sample

03_Midterm2-Sample - 3 The cost function in thousands of...

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University of California, Riverside Department of Mathematics Midterm 2 Mathematics 9A - First Year of Calculus Sample 3 Instructions: This exam has a total of 100 points. You have 50 minutes. You must show all your work to receive full credit You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed to use books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. Find f 0 ( x ) , if (a) (6 points) f ( x ) = q x ° 1 x +1 (b) (7 points f ( x ) = x sin ° 1 x ± (c) (7 points) f ( x ) = (2 x + 1) p 2 cos x ° 1 2. (20 points) Find an equation of the tangent line to the curve ( x 2 + y 2 ) 2 = ( x ° y ) 2 at the point (1 ; 0)
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Unformatted text preview: 3. The cost function, in thousands of dollars, of producing x items of a commodity is C ( x ) = x 3 & 6 x 2 + 15 x: (a) (10 points) Find the marginal cost function. (b) (10 points) Find C (100) and explain its meaning. What does it predict? 1 4. (20 points) A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft/sec. How fast is the top of the ladder sliding down the wall then? 5. (20 points) Use a linear approximation to estimate the given number. (8 : 06) 2 = 3 2...
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