proof using IVT

**zebra2147** · October 28th 2010, 05:38 PM

My professor assigned this exercise and I'm not really sure how to get it started.

Suppose $f(a,b)<0$ and $f(c,d)>0$ . Let $\phi : [0,1]\rightarrow R^2$ be determined by $\phi (t)=(1-t)(a,b)+t(c,d)$ . Apply Bolzano's Intermediate Value Theorem to $g=f(\phi )$ .

Any guidance would be appreciated.

**Drexel28** · October 28th 2010, 08:35 PM

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

**zebra2147** · October 31st 2010, 08:20 AM

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

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