Question 1071558
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<pre>
The volume is V(x) = x*(4-2x)*(3-2x) = x*(4x^2 -2x*(4+3) + 12)) = x*(4x^2 - 14x + 12) = 4x^3 - 14x^2 + 12x.


Take the derivative:

V'(x) = 12x^2 - 28x + 12 

Make it equal to zero:

12x^2 - 28x + 12 = 0,

3x^2 - 7x + 3 = 0,

{{{x[1,2]}}} = {{{(7 +- sqrt(49 - 4*3*3))/(2*3)}}} = {{{(7 +- sqrt(13))/6}}}.


{{{x[1]}}} = 1.768 (approximately), and it is clear that this root doesn't work.

{{{x[2]}}} = 0.566 (approximately.


<U>Answer</U>. The volume is maximal at x = 0.566 m.
</pre>


This solution is pretty straightforward and should not be difficult for you.