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t3(5)

# t3(5) - t weeks from the present to be x = 2 2 t(a ±ind...

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Methods of Calculus, Test 3I March 29, 2002 Instructions: Write your complete solutions in your exam book. Do not write on this paper. This is a closed-book test. No calculators are allowed to be used. You are not required to simplify your answers. (1) Differentiate the functions. (a) f ( x ) = x 3 (1 + 2 x - x 4 ) 5 (b) f ( x ) = x 3 1 + 2 x - x 4 (c) f ( x ) = 4 e (1+5 x ) (d) f ( x ) = ln(1 + 2 x - x 4 ) (2) Find ∂f ∂x and ∂f ∂y for f ( x, y ) = 2 x + 3 y - xy . (3) The profit function for a firm is P = 2 x + 3 ln x where x is the number of units produced and sold. The firm expects the production level at
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Unformatted text preview: t weeks from the present to be x = 2 + 2 t . (a) ±ind the marginal pro²t, dP dx . (b) ±ind the time rate of change of pro²t, dP dt . (c) How fast (with respect to time) are pro²ts changing when t = 2? (4) ±or each function, ²nd the values of x where f ( x ) has a possible relative maximum or minimum point. Use the second derivative to determine the nature of the function at these points. (a) f ( x ) = 1-x e x (b) f ( x ) = 10-e-3 x-6 x...
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