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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 8E

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Need help on this practice exam, little confused on c) and d)

Let f(x, y) = 2y² – x². Compute the following:
(a) Find the gradient V f(x, y). Give your answer using the standard basis vectors i, j. Use symbolic notation and fractions where
needed.
Vf(x, y) =
-2xi + 4yj
i+j.
(b) Find the directional derivative Dµ ƒ(1,2) of ƒ at the point (1, 2) in the direction of the vector u =
Du f(1,2)= 3√2

(c) Give the direction of the fastest rate of increase of ƒ at the point P(1, 2). Give your answer as a unit vector using the standard
basis vectors i, j. Use symbolic notation and fractions where needed.
Direction of fastest increase of f at P is given by:
(d) Give the maximal value of the directional derivative of f at P(1, 2).
Answer =

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