Here's the question you clicked on:

## mskyeg Group Title Miguel is designing shipping boxes that are rectangular prisms. The shape of one box, with height h in feet, has a volume defined by the function V(h) = h(h – 10)(h – 8). What is the maximum volume for the domain 0 < h < 10? Round to the nearest cubic foot. 2 years ago 2 years ago

• This Question is Closed
1. Hero

Are you in Calculus?

2. mskyeg

No im in Algebra 2

3. mskyeg

Hello?

4. mskyeg

@Hero left and i really need to get this done do you think you can help?

5. Mertsj

|dw:1352079518387:dw|

6. Mertsj

This function will have a maximum when h^2-18x + 80 is a maximum.

7. mskyeg

so how do i solve it?

8. freewilly922

\[h^2 -18x +80\] is an open up parabola so doesn't have a max. Is this problem the type they will let you use graphing calculators on the assessment?

9. mskyeg

thankfully yes so do i just enter that equation into a calculator

10. Mertsj

But it does have a local maximum on the interval from 0 to 10

11. freewilly922

If you can graph the function on the calculator there is usually a root finder or a point finder. Use this. @Mertsj, yes, but the local maximum of the function you gave \[h^2-18x +80\] will then be at 0 or 10 since it is an open up parabola. If you graph the cubic the local max they are looking for is between 0 and 8 since |dw:1352080536936:dw|

12. freewilly922

Unless you meant the local min of the parabola?

13. mskyeg

These are the possibl answers how do i answer the question and find out which one it is 10 ft^3 107 ft^3 105 ft^3 110 ft^3

14. freewilly922

Ok, if you can graph the function \[v(h) = h(h-8)(h-8)\] most calculators can find the points t they graphed, so you need to find the point that they ask for.... the maximum volume for the domain. Then ask yourself what is this. This is the height that gives you the maximum volume for that domain. You need the volume associated with it to choose an answer. They give you a function that gives you a volume when you plug into it a height. The trick is using your calculator to find the max.

15. mskyeg

I tried plugging it into the calculator and it says that its not valid