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
f1(0) = 2, f2(0) = 3, g1(0) = 3, g2(0) = 2
f1(1) = 6, f2(1) = 2, g1(1) = 2, g2(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
f1(t).g2(t) - f2(t).g1(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...