Well, arent constant functions just fascinating? They are both increasing and decreasing, yet neither strictly increasing nor strictly decreasing. Amazing how we take so many things for granted, only to find, on closer inspection, that we have been mistaken all along.

]]>PS: I really do appreciate the help you guys give.

]]>when x1 < x2 then f(x1) ≤ f(x2)

Hence, if **y=f(x)** is non-increasing, then there exist x1 < x2 such that f(x1) > f(x2). But a constant function cannot possibly have f(x1) > f(x2). Therefore a constant function cannot be non-increasing.

By a similar argument a constant function cannot be non-decreasing either. Therefore it must be both increasing and decreasing.

]]>A Constant Function neither increases nor decreases:

You realize that this is wrong? In fact, a Constant Function is both increasing and decreasing (but not strictly) along its whole domain.

Think about it.

]]>Hopefully that covers it

]]>Or is that complicating things too much?

]]>According to the new definition, a constant function is increasing and decreasing, rather than neither.

That seems to be a consequence of the definitions, yes. But not strictly increasing or strictly decreasing.

mathsyperson wrote:

Also, I'd say something about how for local extrema, the point should be "in" the interval, rather than on the edge.

For example, with f(x) = x on the interval [1,2], the maximum there would be at x=2. But you wouldn't consider that a local maximum of the function.

In that case there would be NO local extrema?

]]>Also, I'd say something about how for local extrema, the point should be "in" the interval, rather than on the edge.

For example, with f(x) = x on the interval [1,2], the maximum there would be at x=2. But you wouldn't consider that a local maximum of the function.

]]>Glad you went with strictly increasing instead of monotonic. Thanks for the page.

]]>I have redone Increasing Functions

Please check it out and let me know if it passes.

]]>I just read monotonic increasing. Looked it up on wikipedia and they said the same thing for x < y ⇒ f(x) ≤ f(y). Preserving the order they call it.

]]>ie. A constant function counts as increasing, for example.

I learnt the definition on the page as "strictly increasing".

Probably different people use different definitions though.

]]>Look good from here, thanks.

]]>Comments, etc welcome. Help make the pages perfect

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