Byju's Answer
Standard XII
Mathematics
Property 5
If f x =∫1 x ...
Question
If
f
(
x
)
=
∫
x
1
d
t
2
+
t
4
, then
A
f
(
2
)
<
1
3
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B
f
(
2
)
>
1
3
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C
f
(
2
)
=
1
3
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D
f
(
2
)
<
1
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Solution
The correct option is
A
f
(
2
)
<
1
3
f
′
(
x
)
=
1
2
+
x
4
By LMVT
f
′
(
C
)
=
f
(
2
)
−
f
(
1
)
2
−
1
for some
c
ϵ
(
1
,
2
)
⇒
f
(
2
)
=
1
2
+
c
4
as
f
(
1
)
=
0
⇒
1
<
c
<
2
⇒
3
<
2
+
c
4
<
18
⇒
f
(
2
)
<
1
3
Suggest Corrections
0
Similar questions
Q.
If
f
(
x
)
=
∫
x
0
d
t
2
+
t
4
, then
Q.
If
f
(
x
)
,
g
(
x
)
be twice differential functions on
[
0
,
2
]
satisfying
f
′′
(
x
)
=
g
′′
(
x
)
,
f
′
(
1
)
=
2
g
′
(
1
)
=
4
and
f
(
2
)
=
3
g
(
2
)
=
9
, then
Q.
If
α
,
β
≠
0
,
and
f
(
n
)
=
α
n
+
β
n
and
∣
∣ ∣ ∣
∣
3
1
+
f
(
1
)
1
+
f
(
2
)
1
+
f
(
1
)
1
+
f
(
2
)
1
+
f
(
3
)
1
+
f
(
2
)
1
+
f
(
3
)
1
+
f
(
4
)
∣
∣ ∣ ∣
∣
=
K
(
1
−
α
)
2
(
1
−
β
)
2
(
α
−
β
)
2
, then
K
is equal to:
Q.
Which of the following is the phenotypic monohybrid ratio in
F
2
generation?
Q.
Let
f
:
R
→
R
be such that
f
(
2
x
−
1
)
=
f
(
x
)
for all
x
∈
R
. If
f
is continuous at
x
=
1
and
f
(
1
)
=
1
, then
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