I need help with this problem. Can anyone help? Write an equation for the volume, in cubic inches, of a bin with a square base and a height of 2 inches more than 3 times the length of the base. Use the equation to answer the following questions:
a. When is the volume zero? List all possible values of x, that is, the length of a side of the base.
b. Is there a maximum volume? If so, where does it occur?
c. Is there a minimum volume? If so, where does it occur?

Question

I need help with this problem.  Can anyone help?   Write an equation for the volume, in cubic inches, of a bin with a square base and a height of 2 inches more than 3 times the length of the base. Use the equation to answer the following questions: 
a. When is the volume zero? List all possible values of x, that is, the length of a side of the base. 
b. Is there a maximum volume? If so, where does it occur? 
c. Is there a minimum volume? If so, where does it occur?

anonymous · Answer

h= 3x + 2
V =x*x*h = (x^2(3x+2)) =3x^3+2x^2

a.  V=0 when x=0;  all positive x
b.&c.   find V ';   locate V ' =0; determine if V'=0 is the location of max or min by looking at the values of V' on either side: eg. positive to the left, negative to the right of the extremum means a max.

anonymous · Answer

Thank you for your help.  I think I understand it.  I was thinking along those lines.  You confirmed my attempt at the equation, and for a.  I hadn't really gotten to b & c.