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Name: In Exercises 11-18, find the slope of the function's graph at the giv
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Description: In Exercises 11-18, find the slope of the function's graph at the givenpoint. Then find an equation for the line tangent to the graph there.11. f(x) = x + 1, (2, 5)12. f(x) x- 2r, (1, -1)13. g(x) =2 (3, 3)14. g(x)8(2, 2)%3D%3D15. h(t) = , (2, 8)16.

Math

Calculus

In Exercises 11-18, find the slope of the function's graph at the giv point. Then find an equation for the line tangent to the graph there. 11. f(x) = x² + 1, (2, 5) 12. f(x) = x- 2x², (1, –1)

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.9: Direct Variation

Problem 1WE

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Later High School Graduates This is a continuation of Exercise 16. The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.
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. ƒ(x) = x2 + 1, (2, 5) 12. ƒ(x) = x - 2x2, (1, -1) 13. g(x) = x/(x - 2) , (3, 3) 14. 8/ x2 , (2, 2) 15. h(t) = t3, (2, 8) 16. h(t) = t3 + 3t, (1, 4) 17. ƒ(x) = sqrt(x), (4, 2) 18. ƒ(x) = sqrt(x + 1), (8,3).
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