Question

How to interpret the following question:
Graph the curve \(y^2-4x^3+4x^4 = 0\) and use the graph to determine where the extrema of f(x, y) = x occur.

Answer 1

Graph of the curve:
http://www.wolframalpha.com/input/?i=Graph+0+%3D+y%5E2%E2%88%924x%5E3%2B4x%5E4

Answer 2

First thing
\[\Large y^2=4x^3-4x^4\]
Replacing y with -y causes no effect hence graph will be symmetric about x axis

Answer 3

Then?

Answer 4

Plot for 1st quadrant and same will be in 4th quadrant
there will be no graph on negative side

Answer 5

of x axis

Answer 6

I don't understand how to use the graph of \(y^2−4x^3+4x^4=0\) to determine the max/min. of f(x,y)=x