An open box is to be made from a square piece of material, 12 inches on a side, by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box that produces the greatest volume. Answer: 2"by 8" by 8"

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anonymous · Answer

@yun2thejae

anonymous · Answer

@oldrin.bataku

anonymous · Answer

Eww optimization.

anonymous · Answer

lol

anonymous · Answer

ok that was wrong
volume is given by $$V(x)=x(12-2x)^2$$ that should do it
multiply out, take the derivative, set it equal to zero and solve

anonymous · Answer

@satellite73 volume of a square is $$a^3$$ rite?

anonymous · Answer

so how did u get $$x(12-2x)^3$$

anonymous · Answer

|dw:1355890212611:dw|
... so we can model the volume as $V(x)=x(12-2x)^2$. Now we merely need to optimize.\$$\frac1xV(x)=(12-2x)^2$$If we differentiate, we find:$$-\frac1{x^2}V(x)+\frac1xV'(x)=2(12-2x)(-2)$$If we set $V'(x)=0$...$$-\frac1x(12-2x)^2=-4(12-2x)\-\frac1x(12-2x)=-4\12-2x=4x\12=6x\x=2$$