115_sampleexam2

# 115_sampleexam2 - f x = √ 4 x 4 1 x 2-2 x-3 7 The speed...

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Sample Exam 2 1. Use the Second Derivative Test to determine the relative extrema of the function f ( x ) = x + 4 x . 2. Find the derivatives of the following functions. ( i ) . f ( x ) = e x 2 +1 ; ( ii ) . g ( x ) = ln ± ( x - 1) 7 x + 1 x 2 + 1 ² . 3. Let f ( x ) = x 2 e - x deﬁned in ( -∞ , ). Find the intervals of increasing and decreasing of f and relative extrema of f . 4. A culture of bacteria that initially contained 2000 bacteria has a count of 18,000 bacteria after 2hr. Determine the function Q ( t ) that expresses the exponential growth of the number of cells of this bacterium as a function of time t in minutes and use it to ﬁnd the number of bacteria present after 4hr. 5. Let f ( x ) = e - x 2 . Find the intervals of concavity of f and the inﬂection points. 6. Determine the horizontal and vertical asymptotes of
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Unformatted text preview: f ( x ) = √ 4 x 4 + 1 x 2-2 x-3 . 7. The speed of traﬃc ﬂow on a certain stretch of Route US 70 between 6 am to 10 am on a typical weekday is approximated by the function f ( t ) = 2 t-4 √ t + 72 (0 ≤ t ≤ 4) where f ( t ) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6 am. Find the largest speed and smallest speed during this time period. 8. An open box is to have a square base and a volume of 10 cubic feet. If the material for the base costs 5 dollars per square feet, and the material for the four sides costs 2 dollars per square feet. Determine the dimensions of the box with minimum cost. 1...
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## This note was uploaded on 05/13/2008 for the course MATH 115 taught by Professor Bayer,margaret during the Spring '08 term at Kansas.

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