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) dx Find an expression for dy in 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, dy, 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 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) dx Find an expression for dy in 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, dy, 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

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 8T

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Similar questions

Find the distance between the point 3,2 and the line 3x+5y=2.
Is the point (3,0) on the x-axis or y-axis? How do you know?
The point that is 2 units to the left of the y-axis and 4 units above the x-axis has coordinates (______ , ________ ).

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