Sum2010Exam3 - Name MAC 2233 EXAM 3 PART 1 Denitions 1(3...

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Name: MAC 2233 EXAM 3 July 15, 2010 PART 1: Definitions 1. (3 points) Complete the definition: A function f is concave upward on the interval ( a, b ) if 2. (3 points) Define the exponential function f with base b . Include all restrictions on b . 3. (3 points) Complete the definition: The line x = a is a vertical asymptote for the function f if 1
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4. (3 points) Define absolute minimizer of a function f . 5. (3 points) Complete the definition: Let f be a differentiable function. The point x = c is a critical number for f if 2
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PART 2: Problems (show all of your work) 1. (5 points) Find all local maximizers if they exist. If no local maximizers exist, explain why. f ( x ) = - 1 2 x 4 / 5 + 6 local maximizers: 3
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2. (5 points) Suppose f is a function with second derivative f 00 ( x ) = x ( x - 2) 2 ( x + 3) 5 . Suppose further that f satisfies f ( - 3) = 6 f ( - 2) = 7 f ( - 1) = - 3 f (0) = 2 f (1) = - 1 f (2) = 4 f (3) = 1 Find all inflection points of f if they exist. If there are no inflection points, explain why. inflection points: 4
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3. (6 points) Consider the function f ( x ) = x x 2 + 1 .
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