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Mathematics
Mathematics
Problem
Consider
f
(
x
)
=
{
A
(
x
−
1
)
2
+
B
(
x
−
1
)
+
3
,
x
≤
1
ln
x
+
C
,
x
>
1
f(x)=\begin{cases}A(x-1)^{2}+B(x-1)+3,&x\le 1\\ \ln x + C,&x>1\end{cases}
f
(
x
)
=
{
A
(
x
−
1
)
2
+
B
(
x
−
1
)
+
3
,
ln
x
+
C
,
x
≤
1
x
>
1
Find
A
A
A
,
B
B
B
, and
C
C
C
so that
f
f
f
,
f
′
f'
f
′
, and
f
′
′
f''
f
′′
are all continuous at
x
=
1
x=1
x
=
1
.
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