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1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2,1,1). 1) find Vf(2, 1, 1).

1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2,1,1). 1) find Vf(2, 1, 1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2, 1, 1). 1) find Vf (2, 1, 1). 2) Find the equation of the tangent plane to the graph of u at point (2, 1, 1). 3) Find the marginal rate of substitution of x for z along the level curve f = 3, at the point (2; 1; 1). 4) Find the direction of change of input which yields the largest increase in output f at point (2; 1; 1)
Transcribed Image Text:1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2, 1, 1). 1) find Vf (2, 1, 1). 2) Find the equation of the tangent plane to the graph of u at point (2, 1, 1). 3) Find the marginal rate of substitution of x for z along the level curve f = 3, at the point (2; 1; 1). 4) Find the direction of change of input which yields the largest increase in output f at point (2; 1; 1)
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