



 
Hi Rajesh. I am sure you have recognized that a very thin flat box will not hold much volume, and neither will a very tall box with a small base. There must be some value between the extremes that maximizes the volume of the box. Let's consider this algebraically: So the volume of the box is its length times width times depth: Now take the derivative of both sides of this equation with respect to the variable x: You will need to use the chain rule to solve this. Remember that a really narrow box has a small volume, as does a really thin box, but in between these extremes, we find a maximum volume. This is a critical point, so the derivative at the this point is zero. Thus, all you need to do is solve for x by making dV/dx = 0: Solve for x. Cheers,  


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