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Byju's Answer
Standard XI
Mathematics
Differentiability in an Interval
The number of...
Question
The number of points at which
f
(
x
)
=
{
min
(
x
,
x
2
)
,
if
−
∞
<
x
<
1
min
(
2
x
−
1
,
x
2
)
,
if
x
≥
1
is not differentiable is
A
0
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B
1
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C
2
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D
3
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Solution
The correct option is
B
1
f
(
x
)
=
{
min
(
x
,
x
2
)
,
if
−
∞
<
x
<
1
min
(
2
x
−
1
,
x
2
)
,
if
x
≥
1
⇒
f
(
x
)
=
⎧
⎨
⎩
x
,
−
∞
<
x
<
0
x
2
,
0
≤
x
<
1
2
x
−
1
,
1
≤
x
<
∞
⇒
f
′
(
x
)
=
⎧
⎨
⎩
1
,
−
∞
<
x
<
0
2
x
,
0
≤
x
<
1
2
,
1
≤
x
<
∞
⇒
f
′
(
0
−
)
=
1
,
f
′
(
0
+
)
=
0
⇒
f
′
(
1
−
)
=
2
,
f
′
(
1
+
)
=
2
As
f
′
(
0
−
)
≠
f
′
(
0
+
)
, so non differentiable at
x
=
0
But
f
′
(
1
−
)
=
f
′
(
1
+
)
, so differentiable at
x
=
1
Hence,
f
(
x
)
is non differentiable at
1
point.
Suggest Corrections
5
Similar questions
Q.
The number of points at which
f
(
x
)
=
{
min
(
x
,
x
2
)
,
if
−
∞
<
x
<
1
min
(
2
x
−
1
,
x
2
)
,
if
x
≥
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is not differentiable is
Q.
Number of points where
f
(
x
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=
(
1
−
x
)
∣
∣
x
−
x
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∣
+
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Q.
Let
f
(
x
)
=
2
+
√
1
−
x
2
,
|
x
|
≤
1
and
f
(
x
)
=
2
e
(
1
−
x
)
2
,
|
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|
>
1
. The points where
f
(
x
)
is not differentiable are?
Q.
The number of points at which the function
f
(
x
)
=
|
2
x
+
1
|
–
3
|
x
+
2
|
+
|
x
2
+
x
–
2
|
,
x
∈
R
is not differentiable, is
Q.
If
f
(
x
)
=
2
x
+
1
;
x
≤
1
=
x
2
+
2
;
1
<
x
≤
2
=
4
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2
then number of points where
f
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x
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is not differentiable is
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