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JEE Advanced 2013 Paper 2 Mathematics Q13
Mathematics
Problem
Paragraph for Questions 13 and 14 Let
f
:
[
0
,
1
]
→
R
f:[0,1]\to\mathbb R
f
:
[
0
,
1
]
→
R
be a function. Suppose that
f
f
f
is twice differentiable,
f
(
0
)
=
f
(
1
)
=
0
f(0)=f(1)=0
f
(
0
)
=
f
(
1
)
=
0
and
f
′
′
(
x
)
−
2
f
′
(
x
)
+
f
(
x
)
≥
e
x
f''(x)-2f'(x)+f(x)\ge e^x
f
′′
(
x
)
−
2
f
′
(
x
)
+
f
(
x
)
≥
e
x
,
x
∈
[
0
,
1
]
x\in[0,1]
x
∈
[
0
,
1
]
. Which of the following is true for
0
<
x
<
1
0<x<1
0
<
x
<
1
?
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