**Problem Statement:**Find all values of $ x $ and $ y $ such that $ f_x(x, y) = 0 $ and $ f_y(x, y) = 0 $ simultaneously.**Given Function:**\[ f(x, y) = x^2 + 4xy + y^2 - 18x - 24y + 13 \]**Solution Format:**\[ (x, y) = \left( \boxed{\phantom{x}} \right) \]Note: A cross mark indicates that the provided solution is incorrect or missing.

To find all values of such that simutaneously.

Answered: Find all values of x and y such that…

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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Question

**Problem Statement:**

Find all values of $ x $ and $ y $ such that $ f_x(x, y) = 0 $ and $ f_y(x, y) = 0 $ simultaneously.

**Given Function:**

\[ f(x, y) = x^2 + 4xy + y^2 - 18x - 24y + 13 \]

**Solution Format:**

\[ (x, y) = \left( \boxed{\phantom{x}} \right) \]

Note: A cross mark indicates that the provided solution is incorrect or missing.

Expert Solution

Step 1: Define the problem.

To find all values of $straight x space and space straight y$ such that $straight f subscript straight x open parentheses straight x comma space straight y close parentheses equals 0 space and space straight f subscript straight y open parentheses straight x comma space straight y close parentheses equals 0$ simutaneously.

$straight f open parentheses straight x comma space straight y close parentheses equals straight x squared plus 4 xy plus straight y squared minus 18 straight x minus 24 straight y plus 13$