Comment on The "Soft Maximum" functionparentComments−ntownsend16yNo, in this case, a convex function is one where you can draw a straight line between any two points on its graph and not have the line intersect the graph at a third point.−pieceofpeace16yYou are not contradicting what fgimenez said, its the same condition stated differently.edit: if two statements are not essentially same (and I am wrong), could you please explain it.−jamii16yThe logarithm function is convex by this definition but has no maximum/minimum point and never has 0 derivative.
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No, in this case, a convex function is one where you can draw a straight line between any two points on its graph and not have the line intersect the graph at a third point.
You are not contradicting what fgimenez said, its the same condition stated differently.
edit: if two statements are not essentially same (and I am wrong), could you please explain it.
The logarithm function is convex by this definition but has no maximum/minimum point and never has 0 derivative.