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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 60RE

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In exercises 9–14, find all critical numbers and use the Second
Derivative Test to determine all local extrema.
9, f(x)= x+ + 4x³ – 1
(10. f(x) = x* + 4x² + 1
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Exercises 65–70: Find the maximum y-value on the graph of y = f(x). 65. flx) = -x² + 3x – 2 66. f(x) = -x² + 4x + 5 67. f(x) = 5x – x? 68. fx) = -2x² – 2x – 5 69. f(x) = 2x – 3x2 70. f(x) = -4x² + 6x – 9
In Exercises 27–58, find the critical points and the intervals on which the function is increasing or decreasing. Use the First Derivative Test to determine whether the critical point yields a local min or max (or neither).
In Exercises 7–10, write a formula for ƒ ∘ g ∘ h. 7. ƒ(x) = x + 1, g(x) = 3x, h(x) = 4 - x 8. ƒ(x) = 3x + 4, g(x) = 2x - 1, h(x) = x2 9. ƒ(x) = sqrt(x + 1), g(x) = 1 /(x+4) , h(x) = 1 /x 10. ƒ(x) = x + 2 /(3 - x) , g(x) = x2 /(x2 + 1) , h(x) = sqrt(2 - x)
In Exercises 27–50, find the critical points and the intervals on which the function is increasing or decreasing. Use the First Derivative Test to determine whether the critical point is a local min or max (or neither).
In Exercises 53–56, determine where f is increasing. 53. f(x) = |x + 1| 54. f(x) %3D х3 55. f(x) — х4 56. f(x) = %D x4 + x2 + 1
In Exercises 37–40, find a simplified expression for (х). 37. f(x) = 8x - 38x? + 49x – 10, g(x) = 4x – 1 38. f(x) = 2x3 - 9x? – 17x + 39, g(x) = 2x – 3 39. f(x) = 2x4 – 7x + 7x2 - 9x + 10, g(x) = 2x – 5 40. f(x) = 4x4 + 6x3 + 3x – 1, g(x) = 2r? + 1
In Exercises 43–46, find the value(s) of x for which fxgx. f(x)=x2+2x+1,g(x)=5x+19
What is the point of intersection for f(x) = 2* and g(x) = (? A (1,0) (1. 5) (2,4) (0,1) B
In Exercises 129–130, find the inflection points (if any) on the graph of the function and the coordinates of the points on the graph where the function has a local maximum or local minimum value. Then graph the function in a region large enough to show all these points simultane-ously. Add to your picture the graphs of the function’s first and second derivatives. How are the values at which these graphs intersect the x-axis related to the graph of the function? In what other ways are the graphs of the derivatives related to the graph of the function? 1 29. y = x5 - 5x4 - 240 130. y = x3 - 12x2
6x + 1 = -6(1-x) please show work
2 Describe the long run behavior of f(z) = As a + - 00, f(x) V ? As z + 00, f(2) + ( -00
B. Let f(x) = x – x - 4 and g(x) = 2x – 6 4.) Find ()(x - 1) 5.) Find (4) (x)

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