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Consider the function f(x, y) = 2x²-3xy + 8y² + 2x - 4y +4 at the point P(-2,1). a) Find a vector that gives the direction of steepest ascent at P. b) Find a vector that points in a direction of "no change" in the function. c) The graph to the right shows the level curve of f for z 18. Copy the graph onto your own graph paper, and then sketch unit vectors in the direction of the vectors you found in parts (a) and (b) on the graph at point P(-2, 1). Label each vector with (a) or (b) to distinguish them.

Consider the function f(x, y) = 2x²-3xy + 8y² + 2x - 4y +4 at the point P(-2,1). a) Find a vector that gives the direction of steepest ascent at P. b) Find a vector that points in a direction of "no change" in the function. c) The graph to the right shows the level curve of f for z 18. Copy the graph onto your own graph paper, and then sketch unit vectors in the direction of the vectors you found in parts (a) and (b) on the graph at point P(-2, 1). Label each vector with (a) or (b) to distinguish them.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 8E
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2. Consider the function f(x, y) = 2x²-3xy + 8y² + 2x - 4y +4 at the point P(-2, 1). a) Find a vector that gives the direction of steepest ascent at P. b) Find a vector that points in a direction of "no change" in the function. c) The graph to the right shows the level curve of f for z 18. Copy the graph onto your own graph paper, and then sketch unit vectors in the direction of the vectors you found in parts (a) and (b) on the graph at point P(-2, 1). Label each vector with (a) or (b) to distinguish them.
Transcribed Image Text:2. Consider the function f(x, y) = 2x²-3xy + 8y² + 2x - 4y +4 at the point P(-2, 1). a) Find a vector that gives the direction of steepest ascent at P. b) Find a vector that points in a direction of "no change" in the function. c) The graph to the right shows the level curve of f for z 18. Copy the graph onto your own graph paper, and then sketch unit vectors in the direction of the vectors you found in parts (a) and (b) on the graph at point P(-2, 1). Label each vector with (a) or (b) to distinguish them.
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