optimization problem help with factoring

[revisisland24]

Hey guys,

I got V'(x) = 24x^2-12x+1 but that can't be factored. Can anybody point out my mistake?

A rectangular piece of cardboard measures 1 meter by 1/2 meter. Squares are to be cut out from each corner of the rectangle and the sides folded up to make an open-top-box. Determine the dimensions of the box with the largest possible volume.

Can you guys please show your work? I want to know how to do this properly! Thanks a lot.

 

[MarkFL]

You're right, you cannot factor, but is there another method you know of for finding the roots of a quadratic equation?

 

[revisisland24]

You're right, you cannot factor, but is there another method you know of for finding the roots of a quadratic equation?

Yeah, true thanks again!

 

[MarkFL]

One of the roots is outside the domain of the volume function...can you explain why?

 

[revisisland24]

One of the roots is outside the domain of the volume function...can you explain why?

Yeah, because it would make the length negative (or whatever you identify as the side of .5 meters)

 

[MarkFL]

Yes, exactly! Good job of identifying that, so we know we want \(\displaystyle 0<x<\dfrac{1}{4}\).