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Question re cubic function

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moon1130
Average Member

USA
18 Posts

Posted - 09/27/2012 : 22:12:02

Is the cubic function f(x)=x

the only cubic function that has no local maximum or minimum?

Thank you.

royhaas
Moderator

USA
3039 Posts

Posted - 09/28/2012 : 09:23:17

Any translation along the x-axis will look the same.

moon1130
Average Member

USA
18 Posts

Posted - 09/28/2012 : 10:12:18

Thank you for your response.

f(x)=x

and 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.

Ultraglide
Advanced Member

Canada
278 Posts

Posted - 09/28/2012 : 17:44:52

Yes, any cubic of the form f(x) = kx

where k is any real number.

moon1130
Average Member

USA
18 Posts

Posted - 09/28/2012 : 23:57:51

Thank you very much.

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