differentiation problem

[fiery123]

Can someone help me with this question.
The length of a rectangular box is twice its width and it has a surface area of 300 cm^2. Find the dimensions of the box if it is of maximum volume.

[zaza]

1) You know the length in terms of the width.
2) You can work out an expression for the surface area of the box in terms of length, height and width. Hence using 1) you can write this in terms of height and width only. You have a value for this expression.
3) Using the result of 2), you can now write the height in terms of the width only.
4) You know what the volume of the box is in terms of length, height and width (and hence again in terms of width only).
5) Differentiating this gives the rate of change of volume with width. It will be a maximum when the differential is zero.

That should get you pretty much there...

[fiery123]

right thanks.