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Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
Let f x = 1...
Question
Let
f
(
x
)
=
{
1
−
x
+
a
,
x
≤
1
2
x
+
3
,
x
>
1
. If
f
(
x
)
has local minimum at
x
=
1
,
then
a
≤
A
2
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B
3
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C
5
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D
None of these
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Open in App
Solution
The correct option is
C
5
We have
f
(
x
)
=
{
1
−
x
+
a
,
x
≤
1
2
x
+
3
,
x
>
1
Since
y
=
1
−
x
+
a
is decreasing function and
y
=
2
x
+
3
is increasing function
f
(
x
)
will have a local minimum at
x
=
1
If
f
(
1
)
≤
f
(
x
)
for
x
>
1
or if
a
≤
2
x
+
3
for
x
>
1
⇒
a
≤
5
Suggest Corrections
0
Similar questions
Q.
Let
f
(
x
)
=
{
|
x
−
1
|
+
a
,
x
≤
1
2
x
+
3
,
x
>
1
If
f
(
x
)
has local minimum at
x
=
1
and
a
≥
5
then
a
is equal to
Q.
Let
f
:
R
→
R
be defined by
f
(
x
)
=
{
k
−
2
x
,
i
f
x
≤
−
1
2
x
+
3
,
i
f
x
>
−
1
If
f
has a local minimum at
x
=
−
1
, then a possible value of
k
is
Q.
If
f
(
x
)
=
(
x
−
1
)
2
(
x
+
1
)
2
, then the function
f
has
Q.
If
f
(
x
)
=
{
|
x
−
2
|
+
a
,
x
≤
2
3
x
−
1
,
x
>
2
has a local minimum at
x
=
2
, then
a
=
Q.
f
(
x
)
=
{
k
−
2
x
,
i
f
x
≤
−
1
2
x
+
3
,
i
f
x
>
−
1
}
,
if f has a local minimum at x=-1,then k =
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