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In Exercises 19–24, calculate the average rate of change of the given function f over the intervals
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Chapter 3 Solutions
Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th
- Find the derivatives of the functions in Exercises 17ā40. 20. f(t) t? + t ā 2arrow_forwardIn Exercises 11ā18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!arrow_forwardIn Exercises 45ā52, find the domain and range of the function. 45. f(x) ā āŃ 46. g(t) = t4 47. f(x) = xĀ³ 48. g(t) = /2 ā t 49. f(x)= |x| 50. h(s) %3D 1 51. f(x) = 52. g(t) = x2arrow_forward
- Suppose that during the period 1990ā2001, U.S. imports of pasta increased fromĀ 300Ā million pounds in 1990Ā (tĀ = 0)Ā by an average ofĀ 35Ā million pounds/year. Ā (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function ofĀ t, the number of years since 1990. q(t) =Ā Ā Ā Ā (b)Use your model to estimate U.S. pasta imports (in millions of pounds) in 2006, assuming the import trend continued. Ā _________million poundsarrow_forwardSuppose that during the period 1990ā2001, U.S. imports of pasta increased fromĀ 270Ā million pounds in 1990Ā (tĀ = 0)Ā by an average ofĀ 50Ā million pounds/year. (a) Use these data to expressĀ q, the annual U.S. imports of pasta (in millions of pounds), as a linear function ofĀ t, the number of years since 1990. q(t) =Ā Ā Ā Ā (b) Use your model to estimate U.S. pasta imports (in millions of pounds) inĀ 2003, assuming the import trend continued.arrow_forwardIn Exercises 5ā10, find an appropriate graphing software viewing window for the given function and use it to display its graph. The win-dow should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss impor-tant aspects of the function. 5. Ę(x) = x4 - 4x3 + 15 6. Ę(x) = x5 - 5x4 + 10 7. Ę(x) = x sqrt(9 - x2) 8. Ę(x) = x3 /3 - x2/ 2 - 2x + 1 9. Ę(x) = 4x3 - x4 10. Ę(x) = x2(6 - x3)arrow_forward
- Which of the functions graphed in Exercises 1ā6 are one-to-one, and which are not?arrow_forwardIn Exercises 57ā62, find the zeros of Ę and sketch its graph by plotting points. Use symmetry and increase/decrease information where appropriate. 57. f(x) ā Ń ? ā 4 58. f(x) = 2x2 ā 4 %3D %3D 59. f(x) ā Ń 3 ā 4Ń 60. f(x) ā Ń 3 61. f(x) =2 ā x3 62. f(x) = (x ā A)Ā¾i+ate Windarrow_forward- Show that the function f(x) = secx. cscx odd or even %3Darrow_forward
- In Exercises 73ā78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5arrow_forwardThe following graph shows a rough approximation of historical and projected median home prices for a country for the periodĀ 2000ā2024. Here,Ā tĀ is time in years since the start of 2000, andĀ C(t) is the median home price in thousands of dollars. The locations of stationary points and points of inflection are indicated on the graph. Analyze the graph's important features, and interpret each feature in terms of the median home price. The median home price was $_________Ā thousand at the start of 2000 (tĀ = 0). Ā The median home price has two low points; first in the year_______Ā and again in the year___________Ā when it stood at $________Ā thousand; Ā The median home price peaked at the start of the year__________Ā at $_________Ā thousand. Ā The median home price was decreasing most rapidly at the start of the year__________Ā when it was $___________ thousand, and increasing most rapidly at the start of the year__________Ā when it was $_________Ā thousand. Ā Assuming that the trend shown inā¦arrow_forwardFind the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
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