Aimee is shipping a care package to her friend in college, the max volume of the box is mathematically given as
V=1539.6007
<h3>What is the max volume of the box?</h3>Generally, the equation for the height is mathematically given as
V=(20-2x)(40-2x)x
Where x is the height
V=4x^3-120x^2+800x
differentiate v and solve
dv/dx=3x^2-60+200
3x^2-60+200=0
Therefore
x=
x=
x=4.2265
In conclusion, the second differentiation of v and solve we have
d^2v/dx^2=24-240
Hence
d^2v/dx^2< 0
V=(20-2x(40-2x)x
subsitute x
V=(20-2(4.2265))(40-2(4.2265))(4.2265)
V=1539.6007
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