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 Algebra
 Question re cubic function
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moon1130
Senior Member

USA
24 Posts

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

Thank you.
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royhaas
Moderator

USA
3059 Posts

Posted - 09/28/2012 :  09:23:17  Show Profile  Reply with Quote
Any translation along the x-axis will look the same.
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moon1130
Senior Member

USA
24 Posts

Posted - 09/28/2012 :  10:12:18  Show Profile  Reply with Quote
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.
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Ultraglide
Advanced Member

Canada
299 Posts

Posted - 09/28/2012 :  17:44:52  Show Profile  Reply with Quote
Yes, any cubic of the form f(x) = kx where k is any real number.
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moon1130
Senior Member

USA
24 Posts

Posted - 09/28/2012 :  23:57:51  Show Profile  Reply with Quote
Thank you very much.
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