Suppose that f(x) and g(x) are positive functions such that f(x) has a local maximum and g(x) has a local minimum at x=c. Prove that
this means if and that
at x = c
or
I don't know if I am close.
or something along the lines if f(x) is divided by g(x) and is equal to h(x) when f(x) and g(x) have a local minimum and local maximum respectively that would make h(x) also have a local maximum at x = c because if
Well that explains a lot
Then you would not know that there are continuous functions that have no derivatives.
Therefore, you cannot prove this using derivatives.
To say that there is an open neighborhood, , of means where .
In that open interval is an absolute maximum for and is an absolute minimum for .
Okay, I think I have some understanding. I understand the part of absolute maximum and absolute minimum. I still don't understand how this proves is equal to .
I will mark it down as a question I need to return to once I get a a stronger knowledge of the topic.
Thank you