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In Exercises 5–10, find an equation for the tangent to the curve at the given point. Then sketch the curve and tangent together. 5. y = 4 - x, (-1,3) 6. у %3D (х — 1)? + 1, (1, 1) 1 7. y = 2Vx, 8. у %3 , (-1, 1) (1, 2) x2'

In Exercises 5–10, find an equation for the tangent to the curve at the given point. Then sketch the curve and tangent together. 5. y = 4 - x, (-1,3) 6. у %3D (х — 1)? + 1, (1, 1) 1 7. y = 2Vx, 8. у %3 , (-1, 1) (1, 2) x2'

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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33% P 5:35 Asiacell lI.. h Thomas Calculus_ Early Transcende... p 4o In Exercises 5–10, find an equation for the tangent to the curve at the given point. Then sketch the curve and tangent together. 5. у %3D 4 — х2, (-1,3) 6. у %3D (х — 1)? + 1, (1, 1) 7. y = 2Vx, (1, 2) 8. у 3 1 (-1, 1) 9. у %3Dх, (-2, -8) 10. y = . (-2.-) 2, - In Exercises 11–18, find the slope of the function's graph at the given point. Then find an equation for the line tangent to the graph there. 11. f(x) = x² + 1, (2, 5) 12. f(x) — х — 2х?, (1,—1) 8 (2, 2) х 13. g(x) (3, 3) 14. g(x) = x – 2' 15. h(t) = t°, (2, 8) 16. h(t) = t³ + 3t, (1, 4) 17. f(x) = Vx, (4, 2) 18. f(x) = Vx + 1, (8, 3) In Exercises 19–22, find the slope of the curve at the point indicated. 19. у %3D 5х —3x2, x = 1 20. у 3D х3 — 2х + 7, х % -2 1 21. у 3 22. у %3 x – 1 x = 3 x = 0 х — 1° x + 1'
Transcribed Image Text:33% P 5:35 Asiacell lI.. h Thomas Calculus_ Early Transcende... p 4o In Exercises 5–10, find an equation for the tangent to the curve at the given point. Then sketch the curve and tangent together. 5. у %3D 4 — х2, (-1,3) 6. у %3D (х — 1)? + 1, (1, 1) 7. y = 2Vx, (1, 2) 8. у 3 1 (-1, 1) 9. у %3Dх, (-2, -8) 10. y = . (-2.-) 2, - In Exercises 11–18, find the slope of the function's graph at the given point. Then find an equation for the line tangent to the graph there. 11. f(x) = x² + 1, (2, 5) 12. f(x) — х — 2х?, (1,—1) 8 (2, 2) х 13. g(x) (3, 3) 14. g(x) = x – 2' 15. h(t) = t°, (2, 8) 16. h(t) = t³ + 3t, (1, 4) 17. f(x) = Vx, (4, 2) 18. f(x) = Vx + 1, (8, 3) In Exercises 19–22, find the slope of the curve at the point indicated. 19. у %3D 5х —3x2, x = 1 20. у 3D х3 — 2х + 7, х % -2 1 21. у 3 22. у %3 x – 1 x = 3 x = 0 х — 1° x + 1'
33% P 5:36 Asiacell lI.. Thomas Calculus_ Early Transcende... pi Interpreting Derivative Values 23. Growth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number P of cells present at hourly intervals. The num- ber after t hours is shown in the accompanying figure. edge to make a rough per x-unit) at the points P 250 200 150 100 50 2 3 4 5 6 7 a. Explain what is meant by the derivative P'(5). What are its units? b. Which is larger, P'(2) or P'(3)? Give a reason for your answer. c. The quadratic curve capturing the trend of the data points (see Section 1.4) is given by P(t) = 6.10r2 – 9.281 + 16.43. Find the instantaneous rate of growth when t = 5 hours. 24. Effectiveness of a drug On a scale from 0 to 1, the effective- ness E of a pain-killing drug t hours after entering the blood- stream is displayed in the accompanying figure. 1.0 0.8 0.6 0.4 0.2 ngent to the curve at the together. - 1)? + 1, (1, 1) 1 4 5 a. At what times does the effectiveness appear to be increasing? What is true about the derivative at those times? - (-1, 1) b. At what time would you estimate that the drug reaches its - (-2-) maximum effectiveness? What is true about the derivative at -2,- that time? What is true about the derivative as time increases in the 1 hour before your estimated time? ion's graph at the given nt to the graph there. At what points do the graphs of the functions in Exercises 25 and 26 have horizontal tangents? х — 2х?, (1,—1) 25. f(x) = x² + 4x - 1 27. Find equations of all lines having slope -1 that are tangent to the 26. g(x) = x – 3x 8 (2, 2) curve y = 1/(x - 1). 3 + 31, (1, 4) Vx + 1, (8, 3) 28. Find an equation of the straight line having slope 1/4 that is tan- gent to the curve y = Vx. e at the point indicated. Rates of Change 29. Object dropped from a tower top of a 100-m-high tower. Its height above ground after t sec is 100 – 4.91? m. How fast is it falling 2 sec after it is dropped? - 2x + 7, x = -2 An object is dropped from the - 1 X = 0 + 1°
Transcribed Image Text:33% P 5:36 Asiacell lI.. Thomas Calculus_ Early Transcende... pi Interpreting Derivative Values 23. Growth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number P of cells present at hourly intervals. The num- ber after t hours is shown in the accompanying figure. edge to make a rough per x-unit) at the points P 250 200 150 100 50 2 3 4 5 6 7 a. Explain what is meant by the derivative P'(5). What are its units? b. Which is larger, P'(2) or P'(3)? Give a reason for your answer. c. The quadratic curve capturing the trend of the data points (see Section 1.4) is given by P(t) = 6.10r2 – 9.281 + 16.43. Find the instantaneous rate of growth when t = 5 hours. 24. Effectiveness of a drug On a scale from 0 to 1, the effective- ness E of a pain-killing drug t hours after entering the blood- stream is displayed in the accompanying figure. 1.0 0.8 0.6 0.4 0.2 ngent to the curve at the together. - 1)? + 1, (1, 1) 1 4 5 a. At what times does the effectiveness appear to be increasing? What is true about the derivative at those times? - (-1, 1) b. At what time would you estimate that the drug reaches its - (-2-) maximum effectiveness? What is true about the derivative at -2,- that time? What is true about the derivative as time increases in the 1 hour before your estimated time? ion's graph at the given nt to the graph there. At what points do the graphs of the functions in Exercises 25 and 26 have horizontal tangents? х — 2х?, (1,—1) 25. f(x) = x² + 4x - 1 27. Find equations of all lines having slope -1 that are tangent to the 26. g(x) = x – 3x 8 (2, 2) curve y = 1/(x - 1). 3 + 31, (1, 4) Vx + 1, (8, 3) 28. Find an equation of the straight line having slope 1/4 that is tan- gent to the curve y = Vx. e at the point indicated. Rates of Change 29. Object dropped from a tower top of a 100-m-high tower. Its height above ground after t sec is 100 – 4.91? m. How fast is it falling 2 sec after it is dropped? - 2x + 7, x = -2 An object is dropped from the - 1 X = 0 + 1°
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