A natural cubic spline S is defined by:
𝑆
0
(
𝑥
)
=
1
+
𝐵
(
𝑥
−
1
)
−
𝐷
(
𝑥
−
1
)
3
if
1
≤
𝑥
≤
2
S
0
(x)=1+B(x−1)−D(x−1)
3
if 1≤x≤2
𝑆
1
(
𝑥
)
=
1
+
𝑏
(
𝑥
−
2
)
−
3
4
(
𝑥
−
2
)
2
+
𝑑
(
𝑥
−
2
)
3
if
2
≤
𝑥
≤
3
S
1
(x)=1+b(x−2)−
4
3
(x−2)
2
+d(x−2)
3
if 2≤x≤3
If
𝑆
S interpolates the data
(
1
,
1
)
,
(
2
,
1
)
,
(
3
,
0
)
(1,1),(2,1),(3,0), find
𝐵
,
𝐷
,
𝑏
,
B,D,b, and
𝑑
d.
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