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37 and 41

37 and 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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37 and 41

### Section 13.1: Relative Extrema **In Problems 5-8**, the derivative of a continuous function \( f \) is given. Find the open intervals on which \( f \) is (a) increasing; (b) decreasing; and (c) find the \( x \)-value(s) of all relative extrema. **In Problems 9-52**, determine where the function is (a) increasing; (b) decreasing; and (c) determine where relative extrema occur. Do not sketch the graph. 1. \( y = x^3 + x \) 2. \( y = 5x^2 - 2x \) 3. \( y = x^4 - 4x^2 + x \) 4. \( y = x^3 - 3x + 1 \) 5. \( y = 2x^3 - 7x^2 + 17 \) 6. \( y = 3x^2 + 2x + 1 \) 7. \( y = x^4 - 2x + 6 \) 8. \( y = \frac{x}{x+1} \) 9. \( y = -x^3 \) 10. \( y = x^2 + 4x + 3 \) 11. \( y = 2x^3 - 5x \) 12. \( y = 5x^3 - 9x^2 + 5x - 2 \) 13. \( y = \frac{1}{x^2} - 1 \) 14. \( y = x + \frac{1}{x} \) 15. \( y = 2x^2 + 5x - 2 \) 16. \( y = x^4 - 8x^2 + 12 \) 17. \( y = x^3 - 6x^2 + 12x - 15 \) 18. \( y = 12x^5 + 15x^2 \) 19. \( y = 4x^3 - 3x^4 \) 20. \( y = 3x^2 + 4x^3 \) 21. \( y = \frac{1}{x^2} - \frac{1}{x} \) 22. \( y = \frac{1}{x^
Transcribed Image Text:### Section 13.1: Relative Extrema **In Problems 5-8**, the derivative of a continuous function \( f \) is given. Find the open intervals on which \( f \) is (a) increasing; (b) decreasing; and (c) find the \( x \)-value(s) of all relative extrema. **In Problems 9-52**, determine where the function is (a) increasing; (b) decreasing; and (c) determine where relative extrema occur. Do not sketch the graph. 1. \( y = x^3 + x \) 2. \( y = 5x^2 - 2x \) 3. \( y = x^4 - 4x^2 + x \) 4. \( y = x^3 - 3x + 1 \) 5. \( y = 2x^3 - 7x^2 + 17 \) 6. \( y = 3x^2 + 2x + 1 \) 7. \( y = x^4 - 2x + 6 \) 8. \( y = \frac{x}{x+1} \) 9. \( y = -x^3 \) 10. \( y = x^2 + 4x + 3 \) 11. \( y = 2x^3 - 5x \) 12. \( y = 5x^3 - 9x^2 + 5x - 2 \) 13. \( y = \frac{1}{x^2} - 1 \) 14. \( y = x + \frac{1}{x} \) 15. \( y = 2x^2 + 5x - 2 \) 16. \( y = x^4 - 8x^2 + 12 \) 17. \( y = x^3 - 6x^2 + 12x - 15 \) 18. \( y = 12x^5 + 15x^2 \) 19. \( y = 4x^3 - 3x^4 \) 20. \( y = 3x^2 + 4x^3 \) 21. \( y = \frac{1}{x^2} - \frac{1}{x} \) 22. \( y = \frac{1}{x^
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