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^336x^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?

precalculus  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.

precalculus  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 xaxis) and I don't know how to find the maximum value for a parabola like that.

precalculus  bobpursley, Friday, September 18, 2009 at 3:46am
volume=b*b*h
= (362x)^2 x
= (1296144x+4x^2)x
I don't get the same equation as you

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

precalculus  bobpursley, Friday, September 18, 2009 at 3:47am
no, you had a 36 term.

precalculus  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.

precalculus  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.

precalculus  bobpursley, Friday, September 18, 2009 at 4:14am
graphing y=4x^3144x^2+1296x
I get a clear maximum around x=5.7

precalculus  perry, Friday, September 18, 2009 at 4:18am
What are your window settings?

precalculus  bobpursley, Friday, September 18, 2009 at 4:28am
x max 10
y max 10000

precalculus  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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