Chapter 5: Exercises with Solutions

Section 5.6 Optimization 5415.6 Exercises1. Find the exact maximum value ofthe function f(x) = −x 2 − 3x.2. Find the exact maximum value ofthe function f(x) = −x 2 − 5x − 2.3. Find the vertex of the graph of thefunction f(x) = −3x 2 − x − 6.4. Find the range of the function f(x) =−2x 2 − 9x + 2.5. Find the exact maximum value ofthe function f(x) = −3x 2 − 9x − 4.6. Find the equation of the axis of symmetryof the graph of the function f(x) =−x 2 − 5x − 9.7. Find the vertex of the graph of thefunction f(x) = 3x 2 + 3x + 9.8. Find the exact minimum value of thefunction f(x) = x 2 + x + 1.9. Find the exact minimum value of thefunction f(x) = x 2 + 9x.10. Find the range of the function f(x) =5x 2 − 3x − 4.11. Find the range of the function f(x) =−3x 2 + 8x − 2.12. Find the exact minimum value ofthe function f(x) = 2x 2 + 5x − 6.13. Find the range of the function f(x) =4x 2 + 9x − 8.14. Find the exact maximum value ofthe function f(x) = −3x 2 − 8x − 1.15. Find the equation of the axis ofsymmetry of the graph of the functionf(x) = −4x 2 − 2x + 9.16. Find the exact minimum value ofthe function f(x) = 5x 2 + 2x − 3.17. A ball is thrown upward at a speedof 8 ft/s from the top of a 182 foot highbuilding. How many seconds does it takefor the ball to reach its maximum height?Round your answer to the nearest hundredthof a second.18. A ball is thrown upward at a speedof 9 ft/s from the top of a 143 foot highbuilding. How many seconds does it takefor the ball to reach its maximum height?Round your answer to the nearest hundredthof a second.19. A ball is thrown upward at a speedof 52 ft/s from the top of a 293 foot highbuilding. What is the maximum heightof the ball? Round your answer to thenearest hundredth of a foot.20. A ball is thrown upward at a speedof 23 ft/s from the top of a 71 foot highbuilding. What is the maximum heightof the ball? Round your answer to thenearest hundredth of a foot.21. Find two numbers whose sum is 20and whose product is a maximum.22. Find two numbers whose sum is 36and whose product is a maximum.23. Find two numbers whose differenceis 12 and whose product is a minimum.1Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/Version: Fall 2007