How do you sketch an area of a function with two inputs? I have no 3D drawing skills what so ever and I'm having trouble sketching this function.
$f(x,y) =\left\{ \begin{array}{ll} \cfrac{4x^3}{y^3} & \mbox{if } 0 < x < 1, x < y \\ 0 & \mbox{else} \end{array} \right.$
I have to sketch the positive area of this function. How do i do this? Is there any program online to do stuff like that? If not, can anyone show me what the graph looks like so i could practice drawing? Thanks in advance.
One simple way, is to set f(x,y) equal to some constant. Then solve for y in terms of x,(or vice versa). Then draw in this contour. Then choose a new value of f and draw a new contour.
In this case the first thing to identify the triangular region where f is non zero.
Then for any value of f, y = k x. So there is a the contours are all lines running through the origin.
The next most interesting piece would be the boundary at y = 1.