Hey everybody!

 

Hopefully someone has tried this without a computer sometime in the last 20 years or so.

 

I want to draw a graph of cartesian equations, without using software. How does one go about doing this?

 

Example:

[math]x^4=x^2y-y^3[/math]

 

I know what it should look like, as I can cheat and graph it online, but assuming my computer explodes tonight, how can I visualize something like this? Do I just plug in x = 0 and solve for y, etc...? Or is there some kind of easier path I should follow?

 

Thanks in advance!

 

Chris

Find the x intercepts by setting y=0 and the y intercepts by setting x=0. Set the first derivative to zero to find the maximums and minimums. Check if the second derivative is positive, negative, or zero at those points to see the concavity.

[math]x^4=x^2y-y^3[/math]; implicit differrentiation and the product rule must be applied. Solve as stated.