Find all points on the graph of 3x2 + 6y² + 3xy = 64 where the tangent line is horizontal. y X. (Give your answer as a comma-separated list of points in the form (*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.) coordinates of the point(s):
Find all points on the graph of 3x2 + 6y² + 3xy = 64 where the tangent line is horizontal. y X. (Give your answer as a comma-separated list of points in the form (*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.) coordinates of the point(s):
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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![**Problem Description:**
Find all points on the graph of the equation \( 3x^2 + 6y^2 + 3xy = 64 \) where the tangent line is horizontal.
**Graph Explanation:**
- The graph is an ellipse centered on the origin of the coordinate plane.
- The horizontal axis is labeled \( x \) and the vertical axis is labeled \( y \).
- The ellipse is outlined in blue.
- There are two horizontal pink lines indicating where the tangent lines are horizontal on the ellipse.
**Instructions:**
Give your answer as a comma-separated list of points in the form \((*,*)\). Express numbers in exact form. Use symbolic notation and fractions where needed.
**Input Field:**
Coordinate of the point(s): [Text Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53439359-1ad8-43a2-9307-2c193a83e82b%2F3fcf2815-838a-467a-b759-778c517c32ba%2Forg88rk_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
Find all points on the graph of the equation \( 3x^2 + 6y^2 + 3xy = 64 \) where the tangent line is horizontal.
**Graph Explanation:**
- The graph is an ellipse centered on the origin of the coordinate plane.
- The horizontal axis is labeled \( x \) and the vertical axis is labeled \( y \).
- The ellipse is outlined in blue.
- There are two horizontal pink lines indicating where the tangent lines are horizontal on the ellipse.
**Instructions:**
Give your answer as a comma-separated list of points in the form \((*,*)\). Express numbers in exact form. Use symbolic notation and fractions where needed.
**Input Field:**
Coordinate of the point(s): [Text Box]
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