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t3(1)

# t3(1) - y = 2 and dy dt = 7(4(20 points f x = 3 x 2-5 e x(a...

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Methods of Calculus, MAC3233 Test 3 March 26, 1993 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 ) = ( x 2 + 3 x - 1)( x - 2 + 5) (b) f ( x ) = 8 - 3 x 2 2 x + 1 (c) f ( x ) = x x 2 + 3 4 (d) f ( x ) = 10 e ( x 2 + x +1) (2) (10 points) Find dy dx if x and y are related by the equation x 2 + y 2 + xy = - 2. (3) (10 points) If x and y are functions of t and are related by the equation 5 y 2 - x 2 y + x 3 = 17 , find dx dt when x = - 1 and
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Unformatted text preview: y = 2 and dy dt = 7. (4) (20 points) f ( x ) = 3 x + 2-5 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) (20 points) f ( x ) = xe 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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