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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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Directional Derivatives and the Gradient Vector
Suppose that f; (0,1) = 3 and f, (0,1) = 2. From the point (0,1), in what direction should you
travel to increase the value of f(x, y) as quickly as possible?
(Hint: v · u = |v||u| cos(8) has its largest value when 0, the angle between vectors v and u, is
0.)
For the same function f (x, y) as in #1, in what direction should you travel to decrease the value
of f(x, y) as quickly as possible?
(Hint: v · u = |v||u| cos(0) has its minimum value when 0, the angle between vectors v and u,
is π.)
For the same function f (x, y) as in #1, in what direction should you travel to keep the value of
f(x, y) constant?
(Hint: v · u = |v||u| cos(8) is 0 when 0, the angle between vectors v and u, is)

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