Chap5 Section6

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 5.6 Optimization 541 Version: Fall 2007 5.6 Exercises 1. Find the exact maximum value of the function f ( x ) = x 2 3 x . 2. Find the exact maximum value of the function f ( x ) = x 2 5 x 2 . 3. Find the vertex of the graph of the function f ( x ) = 3 x 2 x 6 . 4. Find the range of the function f ( x ) = 2 x 2 9 x + 2 . 5. Find the exact maximum value of the function f ( x ) = 3 x 2 9 x 4 . 6. Find the equation of the axis of sym- metry of the graph of the function f ( x ) = x 2 5 x 9 . 7. Find the vertex of the graph of the function f ( x ) = 3 x 2 + 3 x + 9 . 8. Find the exact minimum value of the function f ( x ) = x 2 + x + 1 . 9. Find the exact minimum value of the function f ( x ) = x 2 + 9 x . 10. Find the range of the function f ( x ) = 5 x 2 3 x 4 . 11. Find the range of the function f ( x ) = 3 x 2 + 8 x 2 . 12. Find the exact minimum value of the function f ( x ) = 2 x 2 + 5 x 6 . 13. Find the range of the function f ( x ) = 4 x 2 + 9 x 8 . 14. Find the exact maximum value of the function f ( x ) = 3 x 2 8 x 1 . Copyrighted material. See: 1 15. Find the equation of the axis of symmetry of the graph of the function f ( x ) = 4 x 2 2 x + 9 . 16. Find the exact minimum value of the function f ( x ) = 5 x 2 + 2 x 3 . 17. A ball is thrown upward at a speed of 8 ft/s from the top of a 182 foot high building. How many seconds does it take for the ball to reach its maximum height? Round your answer to the nearest hun- dredth of a second. 18. A ball is thrown upward at a speed of 9 ft/s from the top of a 143 foot high building. How many seconds does it take for the ball to reach its maximum height? Round your answer to the nearest hun- dredth of a second. 19. A ball is thrown upward at a speed of 52 ft/s from the top of a 293 foot high building. What is the maximum height of the ball? Round your answer to the nearest hundredth of a foot. 20. A ball is thrown upward at a speed of 23 ft/s from the top of a 71 foot high building. What is the maximum height of the ball? Round your answer to the nearest hundredth of a foot. 21. Find two numbers whose sum is 20 and whose product is a maximum. 22. Find two numbers whose sum is 36 and whose product is a maximum. 23. Find two numbers whose difference is 12 and whose product is a minimum.

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542 Chapter 5 Quadratic Functions Version: Fall 2007 24. Find two numbers whose difference is 24 and whose product is a minimum. 25. One number is 3 larger than twice a second number. Find two such numbers so that their product is a minimum. 26. One number is 2 larger than 5 times a second number. Find two such num- bers so that their product is a minimum. 27. Among all pairs of numbers whose sum is 10 , find the pair such that the sum of their squares is the smallest pos- sible. 28. Among all pairs of numbers whose sum is 24 , find the pair such that the sum of their squares is the smallest pos- sible.
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