Question 936346
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x = side length of corner squares
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L = 20 - 2x
w = 15 - 2x
h = x
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v = Lwh
v = (20 - 2x)(15 - 2x)x
v = (20*15 - 20*2x - 2*15x + 4xx)x
v = 300x - 40xx - 30xx + 4xxx
v = 4xxx - 70xx + 300x
v = 4x^3 - 70x^2 + 300x
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the graph:
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{{{ graph( 300, 200, -2, 12, -100, 600, 4x^3-70x^2+300x) }}}
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maximum volume occurs at the graph peak, for x approximately = 2.831 inches
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