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]
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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