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Consider the curve which is the graph of the equation x³ + y³ - 3xy = 0. Graph this curve using your favourite software or graphing calculator to see what this looks like! (It will also help you check your work.) 1. Find an expression for dy in terms of x and y, justifying your steps with the appropriate rules. da 2. dy Find all points on the curve whose tangent lines are horizontal. You may use the fact, without justification, that the derivative, d, does not exist at the point (0,0) (convince yourself of this by looking at a graph, but no need to comment on it in your solution here).

Consider the curve which is the graph of the equation x³ + y³ - 3xy = 0. Graph this curve using your favourite software or graphing calculator to see what this looks like! (It will also help you check your work.) 1. Find an expression for dy in terms of x and y, justifying your steps with the appropriate rules. da 2. dy Find all points on the curve whose tangent lines are horizontal. You may use the fact, without justification, that the derivative, d, does not exist at the point (0,0) (convince yourself of this by looking at a graph, but no need to comment on it in your solution here).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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graph as well please
Consider the curve which is the graph of the equation x³ + y³ - 3xy = 0. Graph this curve using your favourite software or graphing calculator to see what this looks like! (It will also help you check your work.) 1. Find an expression for dy in terms of x and y, justifying your steps with the appropriate rules. da 2. dy Find all points on the curve whose tangent lines are horizontal. You may use the fact, without justification, that the derivative, d, does not exist at the point (0,0) (convince yourself of this by looking at a graph, but no need to comment on it in your solution here).
Transcribed Image Text:Consider the curve which is the graph of the equation x³ + y³ - 3xy = 0. Graph this curve using your favourite software or graphing calculator to see what this looks like! (It will also help you check your work.) 1. Find an expression for dy in terms of x and y, justifying your steps with the appropriate rules. da 2. dy Find all points on the curve whose tangent lines are horizontal. You may use the fact, without justification, that the derivative, d, does not exist at the point (0,0) (convince yourself of this by looking at a graph, but no need to comment on it in your solution here).
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