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Test 2 Review

# Test 2 Review - Math 1309 Chapter 10 Graphing and...

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Chapter 10: Graphing and Optimization Review for Test #2 1. Pages 703 (11 – 38) and Page 705 (51 – 72) Use the first derivative test to determine intervals where the function is increasing and decreasing. Find all local extrema. Example: f(x) = 2x 3 – 3x 2 – 12x – 5 2. Page 642 (43 – 48) Find the second derivative for y = (x 2 – 16) 5 3. Page 723 (23 – 60) Find the intervals where f(x) is concave up and concave down. Find all inflection points. Example: f(x) = x 3 – 18x 2 + 10x – 11 4. Page 725 (43 – 46) Find the point of diminishing returns (when the rate of change is optimum). Example: A company estimates that it will sell N(x) units of a product after spending x thousands of dollars on advertising as given by N(x) = - 0.25x 4 + 13x 3 – 180x 2 + 10,000 where 15 < x < 45. What is the point of diminishing returns (when the rate of change is a maximum)? 5. Page 738 (11 – 28) Find all horizontal asymptotes, vertical asymptotes, and holes, if any, for the graph of a. 6

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Test 2 Review - Math 1309 Chapter 10 Graphing and...

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