Questions 2

[frog1944]

Hi,

1. Are we meant to draw diagrams in pencil? Or should we do it in pen (considering they're scanned)?
2. Why when doing inequalities, can I raise e to the power of both sides and the inequality is preserved? Is it because e^x is monotonic increasing AND is greater than 0 for all x?
3. If in part (i) I do some weird derivation, and obtain an additional results than (i) actually asked for (e.g. inequality question asked show x/y + y/x >= 2, I derive the AM-GM inequality for n=2 in the process), and then in (ii) I say using the other result obtained in (i) (e.g. the AM-GM inequality) is that sufficient? Or would I have to derive whatever the result may be again?

Thanks

[RuiAce]

Hi,

1. Are we meant to draw diagrams in pencil? Or should we do it in pen (considering they're scanned)?
2. Why when doing inequalities, can I raise e to the power of both sides and the inequality is preserved? Is it because e^x is monotonic increasing AND is greater than 0 for all x?
3. If in part (i) I do some weird derivation, and obtain an additional results than (i) actually asked for (e.g. inequality question asked show x/y + y/x >= 2, I derive the AM-GM inequality for n=2 in the process), and then in (ii) I say using the other result obtained in (i) (e.g. the AM-GM inequality) is that sufficient? Or would I have to derive whatever the result may be again?

Thanks

You should be drawing them in pen. (Feel free to use pencil and then trace over it.)


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When that happens, it's likely you took the unintended approach. But so long as you don't assume anything you try to prove, it is fine.

[frog1944]

Great! Thanks RuiAce, for the preservation of the inequality must whatever function I'm applying also be greater than 0 for all x, or just the monotonic increasing part is necessary?

[RuiAce]

Great! Thanks RuiAce, for the preservation of the inequality must whatever function I'm applying also be greater than 0 for all x, or just the monotonic increasing part is necessary?

Just the monotonic increasing part suffices. If you think about it, cubing both sides still preserves the inequality even for negative real numbers (and of course \(x^3\) is monotonic increasing).

[frog1944]

Yeah I see what you're saying. Thanks RuiAce, I appreciate it