
proof using IVT
My professor assigned this exercise and I'm not really sure how to get it started.
Suppose $\displaystyle f(a,b)<0$ and $\displaystyle f(c,d)>0$. Let $\displaystyle \phi : [0,1]\rightarrow R^2$ be determined by $\displaystyle \phi (t)=(1t)(a,b)+t(c,d)$. Apply Bolzano's Intermediate Value Theorem to $\displaystyle g=f(\phi )$.
Any guidance would be appreciated.

Guidance with what...is there a question here?

I'm not sure how to use the Intermediate Value Theorem to $\displaystyle g=f(\phi )$.