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Maximizing Box Volume
medium
Difficulty: medium
f(x) Applications
·
20 pts
·
0 solved
Maximizing Box Volume
Problem Statement
Squares of side
x
are cut from a 12×12 sheet to fold an open box.
Find
x
that maximizes the volume
V
(
x
)
=
x
(
12
−
2
x
)
2
.
\text{Squares of side } x \text{ are cut from a 12×12 sheet to fold an open box.} \\ \text{Find } x \text{ that maximizes the volume } V(x)=x(12-2x)^2.
Squares of side
x
are cut from a 12×12 sheet to fold an open box.
Find
x
that maximizes the volume
V
(
x
)
=
x
(
12
−
2
x
)
2
.
Your Answer (variable: x)
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f(x)
Tips
Use standard math syntax:
^
for powers,
*
for multiplication.
Functions: sin, cos, tan, exp, log (natural log), sqrt.
Constants: pi, e.
For antiderivatives you can omit "+ C".
