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Byju's Answer
Standard XII
Mathematics
Singular and Non Singualar Matrices
Let f x = |...
Question
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
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Solution
i
f
f
(
x
)
h
a
s
a
l
o
c
a
l
m
i
n
i
m
u
m
a
t
x
=
1
t
h
a
t
m
e
a
n
s
t
h
a
t
f
(
x
)
i
s
c
o
n
t
i
n
u
o
u
s
f
u
n
c
t
i
o
n
a
t
x
=
1.
s
o
|
x
−
1
|
+
a
=
2
x
+
3
(
a
t
x
=
1
)
a
=
2
+
3
a
=
5
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Similar questions
Q.
Let
f
(
x
)
=
{
1
−
x
+
a
,
x
≤
1
2
x
+
3
,
x
>
1
. If
f
(
x
)
has local minimum at
x
=
1
,
then
a
≤
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.
Let
f
(
x
)
be a polynomial of degree
3
such that
f
(
−
1
)
=
10
,
f
(
1
)
=
6
,
f
(
x
)
has a critical point at
x
=
−
1
and
f
′
(
x
)
has a critical point at
x
=
1
. Then
f
(
x
)
has a local minima at
x
equals 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
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