A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by cutting equal squares of sides `x` from the corners of the sheet and then turning up the projected portions. The value of `x` os that volume of the box is maximum is 1 (b) 2 (c) 3 (d) 4

Answer

3

Explanation

The dimensions of the box after cutting equal squares fo side x on the corner will be 21-2x,16-2x and height x
`V=x(21-2x)(16-2x)
=x (336-74x+4x^(2)=4x^(3)+336x-74x^(2))`
`therefore (dv)/(dx)=12x^(2)+336-148x`
`(dv)/(dx)=0` gives x =0 for which `(d^(2)V)/(dx^(2))` is ve and hence maximum