Please help with the rest of this

Question

An open-box (top open) is made from a rectangular material of dimensions a=12 inch by b=11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume.



Answer 1

v= x(12-2x)(11-2x)

= x(132 -46x +4x^2)

= 132x -46x^2+4x^3

v'= 132 -92x +12x^2 = 0

3x^2 -23x +33 = 0

factor or use the quadratic formula

x =23/6 +/-(1/6)sqr(23^2-12(33))

=about (23 +/-11.533)/6

=about 1.91 inches (ignore the positive square root)

which gives maximum volume

Answer 2

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