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t3(2) - dx dt = 3(4(15 points f x =(2 x e-x(a f x =(b f 00...

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MAC3233 Test 3 November 1, 1993 Name 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. (1) (10 points each) Find f 0 ( x ) for the following (a) f ( x ) = (3 x 2 - 4 x + 1)( x - 2 + 4) (b) f ( x ) = 3 + 5 x 2 3 x - 2 (c) f ( x ) = x 2 x - 1 4 (d) f ( x ) = e ( x 3 ) (e) f ( x ) = ln( x 3 + 2) (2) (10 points) Find dy dx if x and y are related by the equation 2 x 3 + y - 2 y 3 + x = 0. (3) (10 points) If x and y are functions of t and are related by the equation 2 x 2 + y - y 2 + x = 1 , find dy dt when x = 1 and y
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Unformatted text preview: dx dt = 3. (4) (15 points) f ( x ) = (2 + x ) e-x . (a) f ( x ) = ? (b) f 00 ( x ) = ? (c) Find all possible extrema. (d) Use f 00 ( x ) to say whether each answer in (c) is a relative maximum or minimum. (5) (15 points) f ( x ) = 4 x + e-x . (a) f ( x ) = ? (b) f 00 ( x ) = ? (c) Find all possible extrema. (d) Use f 00 ( x ) to say whether each answer in (c) is a relative maximum or minimum. 1...
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