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Byju's Answer
Standard XII
Mathematics
Local Maxima
Consider the ...
Question
Consider the function
y
=
f
(
x
)
=
ln
(
1
+
sin
x
)
with
−
2
π
≤
x
≤
2
π
.
Find local maxima and minima of f(x)
A
maxima at
x
=
π
2
and no minima,
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B
maxima at
−
3
π
2
and no minima,
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C
maxima at
−
3
π
2
and minima at
x
=
π
2
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D
maxima at
x
=
π
2
and minima at
−
3
π
2
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Solution
The correct options are
A
maxima at
x
=
π
2
and no minima,
B
maxima at
−
3
π
2
and no minima,
y
=
ln
(
1
+
sin
x
)
d
y
d
x
=
cos
x
1
+
sin
x
=
0
for extremum.
⇒
x
=
±
π
2
,
±
3
π
2
But at
x
=
−
π
2
,
3
π
2
ln
(
1
+
sin
x
)
is not defined
Thus
x
=
π
2
,
−
3
π
2
d
2
y
d
x
2
=
−
(
1
+
sin
x
)
sin
x
−
cos
x
.
cos
x
(
1
+
sin
x
)
2
=
−
1
1
+
sin
x
<
0
∀
x
∈
the domain of
f
.
Hence both
x
=
π
2
,
and
x
=
−
3
π
2
are point of local maxima.
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Similar questions
Q.
Find the points of local maxima or minima for the function
f(x) =sin
2
x on [0,π]