A question about the minimum/maximum of a convex function

[pinodk]

I would like to be sure in the following, not prove it, just have it confirmed...
If a function f is convex, then it has

1.) only one maximum and no minimum
2.) only one minimum and no maximum

infinity and -infinity are not included.

 

[HallsofIvy]

It's not clear what you are asking. Since you say you want something "confirmed" it would appear you are making a statement: that either one of those two statements can be true for a convex function. That's not correct.

A convex function is a function f, such that the set {(x,y)| y> f(x) } is convex. Given that, on (2) is true.
(1) is true for a concave function.

 

[pinodk]

Oh, ok, I didnt make a clear distinction between a convex and a concave function.

I didnt have a clear definition of convex and concave, so it makes more sense now, given your definition, and concave is then the opposite, and so makes (1) true.

thanks!

 

[HallsofIvy]

In particular, y= x² is a convex function (the set of point above its graph is convex) and y= -x² is a concave function (the set of points above its graph is concave).

 

[Robokapp]

I would like to be sure in the following, not prove it, just have it confirmed...
If a function f is convex, then it has
1.) only one maximum and no minimum
2.) only one minimum and no maximum
infinity and -infinity are not included.

Convex...I knew it's concave up or concave down. Well, imagine the graph of y=x^2 or y=-x^2 depending on what you're talking about. It's a simple visualisation any Algebra 2 student can do...

bah...the guy above me wrote this exact thing.

However, I wonder, is there such a thing as Convex?

 

[benorin]

yes. In terms of functions: convex = concave up & concave = concave down.

I'm guessing that the whole up/down stuff is from a Calculus text by Stewart.