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consider the function f x x in the interval 1 x 1
Question:
Consider the function
f
(
x
)
=
|
x
|
in the interval
−
1
≤
x
≤
1
. At the point
x
=
0
,
f
(
x
)
is:
MHT CET
Updated On:
Jun 23, 2024
(A) Continuous and differentiable
(B) Non - continuous and differentiable
(C) Continuous and non - differentiable
(D) Neither continuous nor differentiable
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The Correct Option is
C
Solution and Explanation
Explanation:
Given,
f
(
x
)
=
|
x
|
|
x
|
=
x
for
x
≥
0
|
x
|
=
−
x
for
x
<
0
At
x
=
0
Left limit
=
0
, Right limit
=
0
,
f
(
0
)
=
0
ASLeft limit = Right limit = Function value
=
0
∴
|
x
|
is continuous at
x
=
0
.NowLeft derivative
(
at
x
=
0
)
=
−
1
Right derivative
(
at
x
=
0
)
=
1
Left derivative
≠
Right derivative
∴
|
x
|
is not differentiable at
x
=
0
Hence, the correct option is (C).
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