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Tardigrade
Question
Mathematics
If the function f(x)=2 x2+3 x+5 satisfies LMVT at x=2 on the closed interval [1, a] then the value of 'a' is equal to.
Q. If the function
f
(
x
)
=
2
x
2
+
3
x
+
5
satisfies LMVT at
x
=
2
on the closed interval
[
1
,
a
]
then the value of '
a
' is equal to_____.
2714
237
Application of Derivatives
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Answer:
3
Solution:
f
′
(
x
)
=
4
x
+
3
Now
f
′
(
2
)
=
11
=
a
−
1
f
(
a
)
−
f
(
1
)
=
a
−
1
(
2
a
2
+
3
a
+
5
)
−
10
11
a
−
11
=
2
a
2
+
3
a
−
5
2
a
2
−
8
a
+
6
=
0
⇒
a
2
−
4
a
+
3
=
0
(
a
−
3
)
(
a
−
1
)
=
0
⇒
a
=
3