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Consider the function (a) Find f(-5, 4). z = f(-5, 4) = -1575 z = f(x, y) = = = x² + 5xy³. (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z = f(x, y) and such that the coefficient of z in g(x, y, z) is 1. The level set g(x, y, z) = z-x^2 - 5xy^3 z = = 0 is the same as the graph of = f(x, y). (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c).

Consider the function (a) Find f(-5, 4). z = f(-5, 4) = -1575 z = f(x, y) = = = x² + 5xy³. (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z = f(x, y) and such that the coefficient of z in g(x, y, z) is 1. The level set g(x, y, z) = z-x^2 - 5xy^3 z = = 0 is the same as the graph of = f(x, y). (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 36E
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Consider the function (a) Find f(-5, 4). z = f(−5, 4) = -1575 (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z = f(x, y) and such that the coefficient of z in g(x, y, z) is 1. The level set g(x, y, z) f(x, y). z = = Z-x^2 - 5xy^3 z = = f(x, y) = x² + 5xy³. = (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c). Vg(x, y, z) = <-2x-5y^3, -15y^2, 1> = 0 is the same as the graph of (d) Use Vg to find a vector perpendicular (or normal) to the graph of z = f(x, y) at the point (-5, 4, -1575). Write your answer as a row vector of the general form (a, b, c). <-310, 1200, 1> (e) Find an equation for the tangent plane to z = f(x, y) at the point (-5, 4, -1575). Enter your answer as an equation. -310x + 1200y + z - 4775 = 0
Transcribed Image Text:Consider the function (a) Find f(-5, 4). z = f(−5, 4) = -1575 (b) Find a function g(x, y, z) whose level zero set is equal to the graph of z = f(x, y) and such that the coefficient of z in g(x, y, z) is 1. The level set g(x, y, z) f(x, y). z = = Z-x^2 - 5xy^3 z = = f(x, y) = x² + 5xy³. = (c) Find the gradient of g. Write your answer as a row vector of the general form (a, b, c). Vg(x, y, z) = <-2x-5y^3, -15y^2, 1> = 0 is the same as the graph of (d) Use Vg to find a vector perpendicular (or normal) to the graph of z = f(x, y) at the point (-5, 4, -1575). Write your answer as a row vector of the general form (a, b, c). <-310, 1200, 1> (e) Find an equation for the tangent plane to z = f(x, y) at the point (-5, 4, -1575). Enter your answer as an equation. -310x + 1200y + z - 4775 = 0
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