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

Question

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

marigirl · Answer

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solomonzelman · Answer

Cubic function doesn't have an absolute max or absolute minimum if that is what you are referring to.

solomonzelman · Answer

We can model a local maximum at (30,12) if you meant that.

marigirl · Answer

use the point (30,12) and find 
𝑦=1/6750 𝑥(𝑥−60)(𝑥−120),

marigirl · Answer

but still it is not the maximum......... prob cuz it doesnt have it (like you said)

solomonzelman · Answer

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).

marigirl · Answer

thanks :)

solomonzelman · Answer

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)

solomonzelman · Answer

Doesn't that function seem to have a local maximum at (30,12)?

solomonzelman · Answer

Or even better,

$y=\left(x-30\right)^3-\left(x-30\right)^2+12$

solomonzelman · Answer

the second part I added, fixes the chape of the local maximum.

marigirl · Answer

great. thanks heaps. I really appreciate it!

solomonzelman · Answer

Sure, yw