SOLUTION: An open box is to be made from a 24 in. by 36 in. piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the side of the cut o

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Question 1033573: An open box is to be made from a 24 in. by 36 in. piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the side of the cut out square so as obtain the maximum volume?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
v=x%2824-2x%29%2836-2x%29
v=x%2824%2A36-72x-48x%2B4x%5E2%29
v=x%2824%2A36-120x%2B4x%5E2%29
v=4x%5E3-120x%5E2%2B864x


dv%2Fdx=12x%5E2-240x%2B864=0
%281%2F12%29%2812x%5E2-240x%2B864%29=0%281%2F12%29
x%5E2-60x%2B72=0


D=%2860%5E2-4%2A72%29
D=3312
D=207%2A16
D=23%2A9%2A16
D=12sqrt%2823%29


x=%2860%2B-+12%2Asqrt%2823%29%29%2F2---------pick what makes sense.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
An open box is to be made from a 24 in. by 36 in. piece of cardboard by cutting out squares of equal size
from the four corners and bending up the sides. Find the side of the cut out square so as obtain the maximum volume?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

v=x%2824-2x%29%2836-2x%29
v=x%2824%2A36-72x-48x%2B4x%5E2%29
v=x%2824%2A36-120x%2B4x%5E2%29
v=4x%5E3-120x%5E2%2B864x


dv%2Fdx=12x%5E2-240x%2B864=0
%281%2F12%29%2812x%5E2-240x%2B864%29=0%281%2F12%29
x%5E2-20x%2B72=0


D=%2820%5E2-4%2A72%29
D=112
D=4%2A28


x=%2820%2B-+2%2Asqrt%2828%29%29%2F2 = 10+%2B-+sqrt%2828%29.---------pick what makes sense.




Figure. Function V =4x%5E3-120x%5E2%2B864x