open box (Im new to this so i have no idea)

Question

 An open-box (top open) is made from a rectangular material of dimensions a=10 inches by b=6 inches by cutting a square of side  at each corner and turning up the sides Determine the value of  that results in a box the maximum volume.

Express the volume  as a function of : V= 

 Determine the domain of the function  of 

Expand the function 

Find the derivative of : V'=

critical point(s) in the domain of V

value of  at the left endpoint is

value of  at the right endpoint is

maximum volume is V=

value of x that maximizes the volume is

Answer 1

Draw a figure.

The volume of the box will be V=x(6-2x)(10-2x).

The maximum volume will occur when dV/dx = 0.