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## Homework Statement

This is a solved problem, but I haven't understood a few things.

I've marked out sections of the solution in white for convenience. The markings are positioned where that particular section

**ends.**

In part (1), how did they just assume

*f*

_{1}(0) = 2, f_{2}(0) = 3, g_{1}(0) = 3, g_{2}(0) = 2*f*_{1}(1) = 6, f_{2}(1) = 2, g_{1}(1) = 2, g_{2}(1) = 6And, in part (4), what is this 'intermediate value theorem' that they've used?

We've just done the basics on vectors, so I have no idea where this 'intermediate value theorem' came from....

Then, in part (2) they say we have to prove that

*f*

_{1}(t).g_{2}(t) - f_{2}(t).g_{1}(t) = 0And in part (4), they just implied the same thing from out of nowhere & voila! The problem's over!

Please explain that too...