# Vertical Sections and Level Curves

1. Nov 16, 2009

### Juggler123

I need to find the vertical sections and level curves of the function z=max(x,y$$^{2}$$) associated with the constants 1,2,3 and 4.

I know that the function defined in this way basically means that f(x,y)=x if x$$\geq$$y$$^{2}$$ or f(x,y)=y$$^{2}$$ if x$$\prec$$y$$^{2}$$

But I don't know where to go from here, I've been able to sketch lots of vertical sections and level curves for 'normal' functions but this is just confusing me. Can anyone help please? Thanks.

2. Nov 16, 2009