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

1. marigirl

|dw:1444251155105:dw|

2. SolomonZelman

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

3. SolomonZelman

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

4. marigirl

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

5. marigirl

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

6. SolomonZelman

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).

7. marigirl

thanks :)

8. SolomonZelman

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)

9. SolomonZelman

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

10. SolomonZelman

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

11. SolomonZelman

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

12. marigirl

great. thanks heaps. I really appreciate it!

13. SolomonZelman

Sure, yw