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Standard XII
Maths
Question
If
f
(
x
)
is an even function and
f
′
(
x
)
exists, then
f
′
(
e
)
+
f
′
(
−
e
)
is
>
0
0
≥
0
<
0
A
<
0
B
>
0
C
0
D
≥
0
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Solution
Verified by Toppr
f
is called even function when
f
(
−
x
)
=
f
(
x
)
So
f
(
−
x
)
−
f
(
x
)
=
0
Differentiating at
x
=
e
we get,
f
′
(
−
e
)
+
f
′
(
e
)
=
0
f
′
(
−
e
)
=
−
f
′
(
e
)
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2
Similar Questions
Q1
If
f
(
x
)
is an even function and
f
′
(
x
)
exists, then
f
′
(
e
)
+
f
′
(
−
e
)
is
View Solution
Q2
If
f
(
x
)
is an odd function and
f
′
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x
)
exists then
f
′
(
e
)
−
f
′
(
−
e
)
is
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Q3
If
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is an even function and
f
′
(
x
)
exists, then
f
′
(
0
)
=
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Q4
Suppose that
f
(
x
)
is a differential function such that
f
′
(
x
)
is continuous,
f
′
(
0
)
=
1
and
f
′
(
0
)
does not exist. Let
g
(
x
)
=
x
f
′
(
x
)
. Then
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Q5
Suppose that
f
(
x
)
is a differentiable function such that
f
′
(
x
)
is continuous,
f
′
(
0
)
=
1
and
f
′
′
(
0
)
does not exist. Let
g
(
x
)
=
x
f
′
(
x
)
. Then,
View Solution