Question

A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).

Hint:

To differentiate \( S \), apply the power rule and the quotient rule where necessary.

Answer 1

The surface area in terms of \( x \) is: \[ S = x^2 + \frac{4V}{x} \] Now, differentiate \( S \) with respect to \( x \): \[ \frac{dS}{dx} = 2x - \frac{4V}{x^2} \]