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Mathematics
Mathematics
Problem
Let
f
:
[
0
,
1
]
→
R
f:[0,1] \rightarrow R
f
:
[
0
,
1
]
→
R
be a twice differentiable function in
(
0
,
1
)
(0,1)
(
0
,
1
)
such that
f
(
0
)
=
3
f(0)=3
f
(
0
)
=
3
and
f
(
1
)
=
5
f(1)=5
f
(
1
)
=
5
. If the line
y
=
2
x
+
3
y=2x+3
y
=
2
x
+
3
intersects the graph of
f
f
f
at only two distinct points in
(
0
,
1
)
(0,1)
(
0
,
1
)
, then the least number of points
x
∈
(
0
,
1
)
x \in (0,1)
x
∈
(
0
,
1
)
, at which
f
′
′
(
x
)
=
0
f''(x)=0
f
′′
(
x
)
=
0
, is
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