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 Question re cubic function

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moon1130 Posted - 09/27/2012 : 22:12:02
Is the cubic function f(x)=xthe only cubic function that has no local maximum or minimum?

Thank you.
4   L A T E S T    R E P L I E S    (Newest First)
moon1130 Posted - 09/28/2012 : 23:57:51
Thank you very much.
Ultraglide Posted - 09/28/2012 : 17:44:52
Yes, any cubic of the form f(x) = kx where k is any real number.
moon1130 Posted - 09/28/2012 : 10:12:18
Thank you for your response.

f(x)=xand its translations along the x-axis will have no local maximum and minimum. Are there any other cubic functions, excluding vertical and horizontal translations of f(x)=x, that have this property of no local maximum or minimum?

Thank you.
royhaas Posted - 09/28/2012 : 09:23:17
Any translation along the x-axis will look the same.

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