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Byju's Answer
Standard XII
Mathematics
Perpendicular Distance of a Point from a Line
fx=mincos x, ...
Question
f
(
x
)
=
min
{
cos
x
,
1
−
sin
x
}
,
−
π
≤
x
≤
π
.
Then which among the following options is/are correct
A
f
(
x
)
is discontinuous at
x
=
0
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B
f
(
x
)
is differentiable at
x
=
π
2
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C
f
(
x
)
is continuous at
x
=
π
2
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D
f
(
x
)
is not differentiable at
x
=
0
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Solution
The correct option is
D
f
(
x
)
is not differentiable at
x
=
0
f
(
x
)
=
min
{
cos
x
,
1
−
sin
x
}
,
−
π
≤
x
≤
π
⇒
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪
⎩
cos
x
,
−
π
≤
x
<
0
1
−
sin
x
,
0
≤
x
<
π
2
cos
x
,
π
2
≤
x
≤
π
Clearly, from the graph,
f
(
x
)
is continuous everywhere, but has sharp corners at the points where the definition changes i.e. at
x
=
0
and
x
=
π
2
∴
f
(
x
)
is not differentiable at
0
and
π
2
.
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0
Similar questions
Q.
If
f
(
x
)
=
min
{
1
,
x
2
,
x
3
}
, then which among the following options is correct
Q.
Let
f
(
x
)
=
1
−
|
cos
x
|
∀
x
∈
R
,
then which among the following options is/are correct?
Q.
If a function
f
(
x
)
is defined as
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
−
x
,
x
<
0
x
2
,
0
≤
x
≤
1
x
2
−
x
+
1
,
x
>
1
,
then which among the following option is correct
Q.
Let
h
(
x
)
=
sec
{
tan
−
1
(
cos
(
sin
−
1
x
)
)
+
cot
−
1
(
sin
(
cos
−
1
x
)
)
3
}
,
where
x
∈
[
−
1
,
1
]
,
then which of the following option(s) is(are) correct?
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
]
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Perpendicular Distance of a Point from a Line
Standard XII Mathematics
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