OR An open box with a square base is to be made out of a given quantity of cardboard of area`\ c^2` square units. Show that the maximum volume of the box is `(c^3)/(6\ sqrt(3))` cubic units.

Explanation

`Rightarrow quad h=frac{c^{2}-x^{2}}{4 x}`


Putting it in (i) we get



`V=frac{x^{2}(c^{2}-x^{2})}{4 x} Rightarrow V=frac{c^{2} x}{4}-frac{x^{3}}{4}`



Differentiating w.r.t. `x` we get



`frac{d V}{d x}=frac{c^{2}}{4}-frac{3 x^{2}}{4}`


...