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Mathematics
Mathematics
Problem
Consider the region
R
(
k
)
R(k)
R
(
k
)
enclosed by the lines
y
=
8
−
x
y=8-x
y
=
8
−
x
,
y
=
k
x
y=kx
y
=
k
x
, the
y
y
y
-axis, and the vertical line
x
=
k
x=k
x
=
k
, where
0
<
k
<
4
0<k<4
0
<
k
<
4
. Find the value of
k
k
k
that produces the largest possible area of
R
(
k
)
R(k)
R
(
k
)
.
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