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t3(3)

# t3(3) - and suppose that P t satisﬁes the diﬀerential...

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MAC3233 Test 3 July 19, 1995 Name Instructions: This is a closed-book, closed-notes test. Do not write your answers on this paper, use separate answer sheets. No calculators are allowed to be used. To receive credit, you must show all work . For the optimization problems, you are required to show why your answer is a minimum or maximum. Some numerical answers may involve the function ln or the number e . 1. (10 points each) Find f 0 ( x ) for the following (a) f ( x ) = (3 x - 9 - 4 x + 1)( x - 2 + 4) (b) f ( x ) = 3 + 2 x 4 x 3 - 2 (c) f ( x ) = ( e x - 1 + ln x ) 4 (d) f ( x ) = e ( x 3 ) (e) f ( x ) = ln( x 3 + 2) 2. (10 points) Write the equation of the tangent line to the graph of y = 2 ln( x - 1) + 10 x at x = 5. 3. (10 points) Let P ( t ) be the number of bacteria present in a culture after t minutes,
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Unformatted text preview: and suppose that P ( t ) satisﬁes the diﬀerential equation P ( t ) = 0 . 453 P ( t ) . Find the formula for P ( t ) if initially there are approximately 10,500 bacteria present. 4. (15 points) f ( x ) = (4-x ) e x . (a) f ( x ) = ? (b) f 00 ( x ) = ? (c) Find the x coordinate of each possible extremum. (d) Use f 00 ( x ) to say whether each answer in (c) is a relative maximum or minimum. 5. (15 points) f ( x ) = 6 x + e-x . (a) f ( x ) = ? (b) f 00 ( x ) = ? (c) Find the x coordinate of each possible extremum. (d) Use f 00 ( x ) to say whether each answer in (c) is a relative maximum or minimum....
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