Review for Test 2Key

# Review for Test 2Key - Review for 2.4 3.3 Show all possible work on this paper Section 2.4 1 Use the chain rule to find dy/dx if y = u 3 2u 2 3 and

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Review for 2.4 – 3.3 Show all possible work on this paper. Section 2.4 1. Use the chain rule to find dy / dx if 3 2 2 3 y u u = + - and 2 1 u x x = + - . 2.4 ( 29 ( 29 ( 29 2 2 2 2 3 4 ; 2 1; 3 1 4 1 2 1 dy du u u x du dx dy x x x x x dx = + = + = + - + + - + 2. Use the general power rule to differentiate ( 29 = - + 2 4 5 3 2 f x x x . Write final answer in radical form with only positive exponents . 2.4 ( 29 ( 29 ( 29 ( 29 - - - + = - + - = - + 3 1 2 4 2 4 3 2 4 1 10 3 5 3 2 5 3 2 10 3 4 4 5 3 2 d x x x x x x dx x x Section 2.5 3. A manufacturer estimates that when x units of a particular item are produced the total cost will be C(x) = + + 2 1 7 114 5 x x and that all x items will be sold when the price is p(x) = ( 29 - 1 80 4 x dollars per unit. Determine for the 26 th item [a] its marginal cost and [b] its marginal revenue. 2.5 3. a. \$17 Marginal Cost: C’(x) = + 2 7 5 x C’(25) = \$17 Marginal Revenue: R(x) = x[p(x)] = - 2 1 20 4 x x b. \$7.50 R’(x) = - 1 20 2 x R’(25) = 20 – 25 / 2 = \$7.50 4. Approximate by increments how much the function 6 ( ) 14 3 p t t = - + will change as t increases from 5 to 5.2. 2.5 4. 0.01875 ( 29 ( 29 ( 29 ( 29 - - - + = + + = + 1 2 2 6 ' 14 6 3 0 6 3 1 3 p t t t f’(5) = ( 29 = = + 2 6 6 3 64 32 3 5 t = 5.2 - 5 = 0.2 ( 29 f 3 0.2 0.01875 32 ∆ ≈ = 5. The daily output at a certain factory is Q(L) = 300L 3/5 units, where L denotes the size of the labor force measured in worker hours. Currently, 280 worker-hours of labor are used each day. Estimate the number of additional worker-hours of labor that will be needed to increase daily

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## This note was uploaded on 01/04/2012 for the course MAC 2233 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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Review for Test 2Key - Review for 2.4 3.3 Show all possible work on this paper Section 2.4 1 Use the chain rule to find dy/dx if y = u 3 2u 2 3 and

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