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3. Consider the curve which is the graph of the equation r³+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.) (a) Find an expression for din terms of x and y, justifying your steps with the appropriate rules. (b) 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).

3. Consider the curve which is the graph of the equation r³+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.) (a) Find an expression for din terms of x and y, justifying your steps with the appropriate rules. (b) 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).

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.4: Writing And Graphing Equations Of Lines
Problem 80E
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3. 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.) (a) Find an expression for din terms of x and y, justifying your steps with the appropriate rules. (b) 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:3. 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.) (a) Find an expression for din terms of x and y, justifying your steps with the appropriate rules. (b) 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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