Number 20 In Exercises 19-24, a function z =f(x,y) and a polnt P aregiven.(a) Find the direction of maximal Increase offat P.(b) What is the maximal value of D,fat P?(c) Find the direction of minimal increase of f at P.(d) Glve a direction U such that Drf= 0 at P.Note: these are the same functions and points as in Exercises19. f(x y) -xy + xy + xy, P= (2.1)20. (x, y) = sin x cos y, P4 31.21. f(x. y) =P (1,1).22. (x.y)-4x + 3y, P (5.4).23. f(x.y) x + 2y-xy- 7x, P (4,1)24. f(x y)xy 2x, P= (1.1)

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Answered: () 20. (x. y) = sinx cos y, P =

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() 20. (x. y) = sinx cos y, P =

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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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.