Need help on another optimization problem

[jzq]

Problem: An open top box is constructed from a sheet of material by cutting equal squares from each corner and folding up the edges. If the sheet of material measures 14 inches by 9 inches, find the dimension x which represents the length of one side of the square that should be cut off so that the volume is maximized.

Work Done (Please Check!):

Length: $$L(x)=-2x+14$$

Width: $$W(x)=-2x+9$$

Height: $$H(x)=x$$

Volume: $$V(x)=4x^{3}-46x^{2}+126x$$

This is where I am stuck:

$$V'(x)=12x^{2}-92x+126$$

I need to factor out the derivative so that I can get the critical numbers. Unless I did something wrong, from what I got above it's not going to be whole numbers. I always have problems with fractions.

 

[Xerxes1986]

Problem: An open top box is constructed from a sheet of material by cutting equal squares from each corner and folding up the edges. If the sheet of material measures 14 inches by 9 inches, find the dimension x which represents the length of one side of the square that should be cut off so that the volume is maximized.

Work Done (Please Check!):

Length: $$L(x)=-2x+14$$

Width: $$W(x)=-2x+9$$

Height: $$H(x)=x$$

Volume: $$V(x)=4x^{3}-46x^{2}+126x$$

This is where I am stuck:

$$V'(x)=12x^{2}-92x+126$$

I need to factor out the derivative so that I can get the critical numbers. Unless I did something wrong, from what I got above it's not going to be whole numbers. I always have problems with fractions.

this is more of a calc problem than physics

get a ti89 :D

i get the zeroes as 5.88 and 1.79...if you take the 2nd derivative you can find out which is the max and which is the min...

 

[jzq]

Thanks for your advice and solution.

P.S. No offense, this forum deals with all subjects even though it is called Physics Forums. This is college homework so that is why I posted this here. If you look at other threads in this section, you will also find other calculus problems. And about the TI-89, I can't use calculators on tests.

 

[Xerxes1986]

Thanks for your advice and solution.

P.S. This forum deals with all subjects. This is college homework so that is why I posted this here. If you look at other threads in this section, you will also find other calculus problems. And about the TI-89, I can't use calculators on tests.

if she gives you problems like that she better!

of course if she gives you a similar problem it will easily be factored

basically you just find the zeroes of the derivative function...either with an 89 or using factoring

 

[jzq]

Yea, I think it's ridiculous that we can't use calculators on tests. Fortunately, this is only a practice problem. Hopefully they won't have something like this on the test. Thanks again!