Let f(x, y) = 2y² - x². Compute the following: (a) Find the gradient Vf(x, y). Give your answer using the standard basis vectors i, j. Use symbolic notation and fractions needed. Vf(x, y) = (b) Find the directional derivative Duf(1, 2) of f at the point (1, 2) in the direction of the vector u = i + j. Du f(1,2)= (c) Give the direction of the fastest rate of increase of f 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=

Let f(x, y) = 2y² - x². Compute the following: (a) Find the gradient Vf(x, y). Give your answer using the standard basis vectors i, j. Use symbolic notation and fractions needed. Vf(x, y) = (b) Find the directional derivative Duf(1, 2) of f at the point (1, 2) in the direction of the vector u = i + j. Du f(1,2)= (c) Give the direction of the fastest rate of increase of f 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=

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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