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- Aug 14th 2006, 12:00 AMMathsThiefModelling and Problem Solving Calculus
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- Aug 14th 2006, 06:33 AMCaptainBlackQuote:

Originally Posted by**MathsThief**

$\displaystyle \alpha x^3 + \beta x^2 + \gamma x +\delta$, with $\displaystyle \alpha<0$.

Arrange for the first to have a local minimum at $\displaystyle x=5$, and the

second to have a local maximum at the same point, and then arrange that the

two curves are equal at the point. Then if this point is the join the merged curve will be smooth.

Now arrange for the total length of the merged curve to be 20km

RonL - Aug 15th 2006, 12:17 AMMathsThief
Thanks! Please delete thread this i'm done now. ^_^

- Aug 15th 2006, 04:00 AMCaptainBlackQuote:

Originally Posted by**MathsThief**

RonL - Aug 15th 2006, 08:07 AMThePerfectHacker
Do not delete your question, ever!

That violates the principles by which this site was founded. :mad:

-=USER WARNED=- - Apr 17th 2010, 05:02 PMfaux
I'm attempting a similar problem -- would you be able to expand upon that? I'm having problems manipulating my cubic function(s) to fit accordingly (namely, setting local max/mins and getting them to lie between two points).

Also, those two cubic function would only cover the first 'part' of the 'profile', and not the final slope downwards -- how would you go about that?

Many thanks,

Faux