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

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.5: Applications

Problem 11EQ

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Question

Number 20

In Exercises 19-24, a function z =
f(x,y) and a polnt P are
given.
(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 Exercises
19. f(x y) -xy + xy + xy, P= (2.1)
20. (x, y) = sin x cos y, P
4 3
1.
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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