Question

a manufacturer of open tin boxes wishes to make use of tin with dimension 10 inches by 20 inches by cutting equal squares from the four corners and turning up sides. find the lengths of the side of the square to be cut out if an open box having the largest possible volume is to be obtained from each piece of the tin.

Answer 1

v = x(10-2x)(20-2x)
dv/dx = 4(3x^2-30x+50)
Now just find where dv/dx=0 and decide whether that's a minimum or a maximum.