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Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² + 4xy + y² - 18x - 24y + 13 (x, y) = (3,3

Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² + 4xy + y² - 18x - 24y + 13 (x, y) = (3,3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find all values of \( x \) and \( y \) such that \( f_x(x, y) = 0 \) and \( f_y(x, y) = 0 \) simultaneously. \[ f(x, y) = x^2 + 4xy + y^2 - 18x - 24y + 13 \] \[ (x, y) = \left( \begin{array}{c} 3, 3 \\ \end{array} \right) \quad \textcolor{red}{\text{✗}} \] In this problem, we seek the critical points of the given multivariable function by finding where both partial derivatives (with respect to \( x \) and \( y \)) are zero. The attempted solution \((3, 3)\) is indicated as incorrect by a red cross.
Transcribed Image Text:Find all values of \( x \) and \( y \) such that \( f_x(x, y) = 0 \) and \( f_y(x, y) = 0 \) simultaneously. \[ f(x, y) = x^2 + 4xy + y^2 - 18x - 24y + 13 \] \[ (x, y) = \left( \begin{array}{c} 3, 3 \\ \end{array} \right) \quad \textcolor{red}{\text{✗}} \] In this problem, we seek the critical points of the given multivariable function by finding where both partial derivatives (with respect to \( x \) and \( y \)) are zero. The attempted solution \((3, 3)\) is indicated as incorrect by a red cross.
Expert Solution
Step 1: Determine the given information

The given function f open parentheses x comma space y close parentheses equals x squared plus 4 x y plus y squared minus 18 x minus 24 y plus 13.

The aim is to find all values of x and y such that f subscript x open parentheses x comma space y close parentheses equals f subscript y open parentheses x comma space y close parentheses equals 0.

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