Please help with open box problem

Question

An open-box is made from a rectangular material of dimensions a=8 inches by b=5 inches by cutting a square of side x at each corner and turning up the sides. Determine the value of x that results in a box the masimum value.

1)express the volume V as a function of x: V=

2)determine the domain of the function V of x(in interval form):

3)expand the function V for easier differentiation: V=

4)find the derivative of the function of V: V’=

5)find the critical point(s) it the domain V:

6) the Value of V at the left endpoint is:

7) the value of V at the right endpoint is:

8) the maximum volume is V=

9) answer the original question. The value of x that maximizes the volume is:

Answer 1

The volume of the box will be V=(8-2x)(5-2x)x

dV/dx=0=10-13x+3x²

^{Possible roots are 1 and 3 1/3...both of which will work}

^{You should be able to answer all the questions with the information provided.}