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Byju's Answer
Standard XII
Mathematics
One-One into Function
The total num...
Question
The total number of local maxima and local minima of the function
f
(
x
)
=
{
(
2
+
x
)
3
,
−
3
<
x
≤
−
1
x
2
3
,
−
1
<
x
<
2
is
A
2
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B
0
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C
3
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D
1
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Solution
The correct option is
A
2
We have,
f
(
x
)
=
{
(
2
+
x
)
3
,
−
3
<
x
≤
−
1
x
2
3
,
−
1
<
x
<
2
⇒
f
′
(
x
)
=
⎧
⎨
⎩
3
(
x
+
2
)
2
.
−
3
<
x
≤
1
2
3
x
−
1
3
;
−
1
<
x
<
2
Clearly
f
′
(
x
)
changes its sign at
x
=
–
1
from +ve to –ve and so
f
(
x
)
has local maxima at
x
=
–
1
.
lso
f
′
(
0
)
does not exist but
f
′
(
0
−
)
<
0
and
f
′
(
0
+
)
>
0
, it can only be inferred that
f
(
x
)
has a possibility of a minima at
x
=
0
.
Hence the given function has one local maxima at
x
=
–
1
and one local minima at
x
=
0
.
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0
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