Is it possible to model a Cubic so that it has a maximum of (30,12). See my drawing below

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Is it possible to model a Cubic so that it has a maximum of (30,12). See my drawing below

Mathematics
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Cubic function doesn't have an absolute max or absolute minimum if that is what you are referring to.
We can model a local maximum at (30,12) if you meant that.

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use the point (30,12) and find 𝑦=1/6750 𝑥(𝑥−60)(𝑥−120),
but still it is not the maximum......... prob cuz it doesnt have it (like you said)
here: desmos.com use that calculator to graph your equation, and you will see that (30,12) is not the local maximum (in fact not even a point on the function).
thanks :)
You can do this: \(y=\left(x-30\right)^3+12\) (Shift a parent function x³ by 30 units to the right, and by 12 units up)
Doesn't that function seem to have a local maximum at (30,12)?
Or even better, \(y=\left(x-30\right)^3-\left(x-30\right)^2+12\)
the second part I added, fixes the chape of the local maximum.
great. thanks heaps. I really appreciate it!
Sure, yw

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