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Mathematics
Mathematics
Problem
For
0
<
k
<
6
0 < k < 6
0
<
k
<
6
, let
R
(
k
)
R(k)
R
(
k
)
be the region in the first quadrant bounded above by
y
=
6
x
−
x
2
y = 6x - x^2
y
=
6
x
−
x
2
and below by
y
=
k
x
y = kx
y
=
k
x
on the interval
0
≤
x
≤
k
0 \le x \le k
0
≤
x
≤
k
. Which value of
k
k
k
yields the largest possible area of
R
(
k
)
R(k)
R
(
k
)
? a)
k
=
3
k=3
k
=
3
b)
k
=
2
k=2
k
=
2
c)
k
=
12
5
k=\frac{12}{5}
k
=
5
12
d)
k
=
5
2
k=\frac{5}{2}
k
=
2
5
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