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Mathematics
Mathematics
Problem
A region
R
(
k
)
R(k)
R
(
k
)
is bounded above by the curve
y
=
4
x
−
x
2
y = 4x - x^2
y
=
4
x
−
x
2
and below by the
x
x
x
-axis on the interval
0
≤
x
≤
k
0 \leq x \leq k
0
≤
x
≤
k
, where
0
<
k
≤
4
0 < k \leq 4
0
<
k
≤
4
. The area of the region is
A
(
k
)
=
∫
0
k
(
4
x
−
x
2
)
d
x
A(k) = \int_{0}^{k} (4x - x^2) \,dx
A
(
k
)
=
∫
0
k
(
4
x
−
x
2
)
d
x
. For which value of
k
k
k
does
R
(
k
)
R(k)
R
(
k
)
have the greatest area? a)
k
=
5
2
k=\dfrac{5}{2}
k
=
2
5
b)
k
=
4
k=4
k
=
4
c)
k
=
2
k=2
k
=
2
d)
k
=
3
k=3
k
=
3
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