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For each function in Exercises 7-28, (a) give of any critical points and classify each point as a relative maximum, a relative minimum, or neither; (b) identify intervals where the function is increasing or decreasing; (c) give the coordinates of any points of inflection; (d) identify intervals where the function is concave up or concave down, and (e) sketch the graph. 7. f(x) = x² - 10x + 2 9. t(x) = -x² + 6x + 7 11. F(x) = 3x² + 4x + 2 13. h(x) = x³ - 27x 15. f(x) = xe3x 8. g(x) = x² + 12x - 4 10. y(x) = -x² - 8x + 1 12. G(x) = 5x² 14. g(x) = x³ 48x - 1 16. b(x) = xe 4x 2x - 3 - - 40. 41.

For each function in Exercises 7-28, (a) give of any critical points and classify each point as a relative maximum, a relative minimum, or neither; (b) identify intervals where the function is increasing or decreasing; (c) give the coordinates of any points of inflection; (d) identify intervals where the function is concave up or concave down, and (e) sketch the graph. 7. f(x) = x² - 10x + 2 9. t(x) = -x² + 6x + 7 11. F(x) = 3x² + 4x + 2 13. h(x) = x³ - 27x 15. f(x) = xe3x 8. g(x) = x² + 12x - 4 10. y(x) = -x² - 8x + 1 12. G(x) = 5x² 14. g(x) = x³ 48x - 1 16. b(x) = xe 4x 2x - 3 - - 40. 41.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Chapter 3: Applications of Differentiation** For each function in Exercises 7–28, perform the following tasks: (a) Provide the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither. (b) Identify intervals where the function is increasing or decreasing. (c) Give the coordinates of any points of inflection. Identify intervals where the function is concave up or concave down. (d) Sketch the graph. 7. \( f(x) = x^2 - 10x + 2 \) 8. \( g(x) = x^2 + 12x - 4 \) 9. \( t(x) = -x^2 + 6x + 7 \) 10. \( y(x) = -x^2 - 8x + 1 \) 11. \( F(x) = 3x^2 + 4x + 2 \) 12. \( G(x) = 5x^2 - 2x - 3 \) 13. \( h(x) = x^3 - 27x \) 14. \( q(x) = x^3 - 48x - 1 \) 15. \( f(x) = xe^{3x} \) 16. \( b(x) = xe^{-4x} \) 17. \( a(x) = \ln(x^2 + 9) \) 18. \( c(x) = \ln(x^2 + 16) \) 19. \( g(x) = x^3 - 6x^2 + 9x + 1 \) 20. \( f(x) = x^3 - 2x^2 - 4x + 3 \) 21. \( k(x) = x^4 - 2x^3 \) 22. \( j(x) = x^4 + 4x^3 \) 23. \( f(x) = 3x - e^x \) 24. \( h(x) = 2x - e^{4x} \) 25. \( q(x) = \frac{8x}{x^2 + 1} \) 26. \( r(x) = \frac{-4}{x^2 + 1} \)
Transcribed Image Text:**Chapter 3: Applications of Differentiation** For each function in Exercises 7–28, perform the following tasks: (a) Provide the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither. (b) Identify intervals where the function is increasing or decreasing. (c) Give the coordinates of any points of inflection. Identify intervals where the function is concave up or concave down. (d) Sketch the graph. 7. \( f(x) = x^2 - 10x + 2 \) 8. \( g(x) = x^2 + 12x - 4 \) 9. \( t(x) = -x^2 + 6x + 7 \) 10. \( y(x) = -x^2 - 8x + 1 \) 11. \( F(x) = 3x^2 + 4x + 2 \) 12. \( G(x) = 5x^2 - 2x - 3 \) 13. \( h(x) = x^3 - 27x \) 14. \( q(x) = x^3 - 48x - 1 \) 15. \( f(x) = xe^{3x} \) 16. \( b(x) = xe^{-4x} \) 17. \( a(x) = \ln(x^2 + 9) \) 18. \( c(x) = \ln(x^2 + 16) \) 19. \( g(x) = x^3 - 6x^2 + 9x + 1 \) 20. \( f(x) = x^3 - 2x^2 - 4x + 3 \) 21. \( k(x) = x^4 - 2x^3 \) 22. \( j(x) = x^4 + 4x^3 \) 23. \( f(x) = 3x - e^x \) 24. \( h(x) = 2x - e^{4x} \) 25. \( q(x) = \frac{8x}{x^2 + 1} \) 26. \( r(x) = \frac{-4}{x^2 + 1} \)
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