frozenstellar, I don't like the style of your proofs. Maybe your markers will...
Yes, in order to use the IVT, you have to pick an interval for question 1. You caught that. But:
Quote:
let x E [0,10] (did this as there was no interval restiction stated in the question)
g(0) < g(x) < g(10)
-109 < g(x) < 461
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This is either meaningless or wrong. Just because x is in [0,10] doesn't mean g(x) is in [g(0),g(10)]. And that is what you said in the above 3 lines.
A proof in math isn't just about reaching the end: it is about getting to the end properly. Especially when you are told where you are supposed to go. =)
There is the same problem in your second "proof".