 #1
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 20
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) = 6
And, 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) = 0
And in part (4), they just implied the same thing from out of nowhere & voila! The problem's over!
Please explain that too...
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