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MHTCET 2016 Math Solved Paper
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© examsnet.com
Question : 5
Total: 50
If Rolle’s theorem for f(x) =
e
x
(sin x - cos x) is verified on
[
π
4
,
5
π
4
]
, then the value of c is
π
3
π
2
3
π
3
π
Validate
Solution:
(b) Given,
f
(
x
)
=
e
x
(
sin
x
−
cos
x
)
⇒
f
′
(
x
)
=
e
x
d
d
x
(
sin
x
−
cos
x
)
+
(
sin
x
−
cos
x
)
d
d
x
(
e
x
)
=
e
x
(
cos
x
+
sin
x
)
+
(
sin
x
−
cos
x
)
e
x
=
2
e
x
sin
x
We know that, if Rolle's theorem is verified,then their exist c ∊
(
π
4
,
5
π
4
)
,
such that
f
′
(
c
)
=
0
∴ 2
e
c
sin c = 0 ⇒ sin c = 0
⇒ C =
π
2
∊
(
π
4
,
5
π
4
)
© examsnet.com
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