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Byju's Answer
Standard XII
Mathematics
Definition of Functions
If fx=min1,x2...
Question
If
f
(
x
)
=
min
{
1
,
x
2
,
x
3
}
, then which among the following options is correct
A
f
(
x
)
is continuous and differentiable everywhere.
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B
f
(
x
)
is not differentiable at two points.
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C
f
(
x
)
is not everywhere continuous.
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D
f
(
x
)
is not differentiable at one point.
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Solution
The correct option is
D
f
(
x
)
is not differentiable at one point.
Drawing curves for
y
=
x
2
,
x
3
,
1
and represnting
min
{
1
,
x
2
,
x
3
}
through a solid line, we get
f
(
x
)
=
min
{
1
,
x
2
,
x
3
}
=
{
x
3
,
x
<
1
1
,
x
≥
1
Clearly,
f
(
1
+
)
=
f
(
1
−
)
=
f
(
1
)
=
1
Hence,
f
(
x
)
is continuous at
x
=
1
But clearly, there is sharp corner at
x
=
1
So,
f
(
x
)
is not differentiable at
x
=
1
.
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0
Similar questions
Q.
If
f
(
x
)
=
m
i
n
{
1
,
x
2
,
x
3
}
then
Q.
If
f
(
x
)
=
m
i
n
{
1
,
x
2
,
x
3
}
, then
Q.
Let
f
(
x
)
=
x
3
−
x
2
+
x
+
1
and
g
(
x
)
=
{
max
{
f
(
t
)
}
,
0
≤
t
≤
x
,
0
≤
x
≤
1
3
−
x
,
1
<
x
≤
2
,
Then which among the following options is/are correct for
g
(
x
)
in
[
0
,
2
]
Q.
Let
f
(
x
)
=
m
i
n
{
1
−
|
x
|
,
x
2
−
1
}
, then
Q.
If
f
(
x
)
=
lim
m
→
∞
lim
n
→
∞
(
1
+
cos
2
m
(
n
!
π
x
)
)
, then which among the following options is/are CORRECT ?
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