Posted by **perry** on Friday, September 18, 2009 at 3:00am.

An open box is made from a square piece of material 36 inches on a side by cutting equal squares from the corners and turning up the sides. Use your calculator to find the maximum volume this box can hold.

I got the equation 4x^3-36x^2+1296x = V

But when I put it in the calculator I don't know how to find the maximum value. How do I find the maximum value of a 3rd degree polynomial like this?

- pre-calculus -
**bobpursley**, Friday, September 18, 2009 at 3:23am
Calculators can...

Did you graph it?

did you take the derivative of it, and solve that?

I have no idea what you are doing with your calculator. I recommend graphing.

- pre-calculus -
**perry**, Friday, September 18, 2009 at 3:26am
I tried graphing but when I put it in I get a negatively shaped parabola (below the x-axis) and I don't know how to find the maximum value for a parabola like that.

- pre-calculus -
**bobpursley**, Friday, September 18, 2009 at 3:46am
volume=b*b*h

= (36-2x)^2 x

= (1296-144x+4x^2)x

I don't get the same equation as you

- pre-calculus -
**perry**, Friday, September 18, 2009 at 3:46am
That's the same exact equation but you took out an x.

- pre-calculus -
**bobpursley**, Friday, September 18, 2009 at 3:47am
no, you had a 36 term.

- pre-calculus -
**perry**, Friday, September 18, 2009 at 3:57am
Oops, that was a typo. I tried taking 4x out and typed in 36x^2. That should be 144x^2. Aka, the same equation as yours.

- pre-calculus -
**perry**, Friday, September 18, 2009 at 4:06am
Can anybody figure out how to find the maximum value on this? -b/2a doesn't work either since it's not a 2nd degree polynomial.

- pre-calculus -
**bobpursley**, Friday, September 18, 2009 at 4:14am
graphing y=4x^3-144x^2+1296x

I get a clear maximum around x=5.7

- pre-calculus -
**perry**, Friday, September 18, 2009 at 4:18am
What are your window settings?

- pre-calculus -
**bobpursley**, Friday, September 18, 2009 at 4:28am
x max 10

y max 10000

- pre-calculus -
**Julie**, Wednesday, April 14, 2010 at 1:14am
An open box is to be made from a flat piece of material 18 inches long and 5 inches wide by cutting equal squares of length xfrom the corners and folding up the sides.

Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.

V=

If we write the domain of the box as an open interval in the form (a,b), then what is a=?

a=

and what is b=?

b=

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