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Byju's Answer
Standard XII
Mathematics
Differentiability in an Interval
The function ...
Question
The function
f
(
x
)
=
cos
−
1
(
4
x
3
−
3
x
)
is
A
always differentiable
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B
not differentiable at 2 points only
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C
not continuous at 2 points only
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D
not differentiable at 4 points only
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Solution
The correct option is
D
not differentiable at 4 points only
l
e
t
f
(
x
)
=
y
=
cos
−
1
(
4
x
3
−
3
x
)
then,
f
(
x
)
has sharp turns at
x
=
−
1
2
,
1
2
and also vertical tangents at
x
=
−
1
,
1
.
Therefore
f
(
x
)
is not differentiable at
x
=
−
1
,
−
1
2
,
1
2
,
1
.
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1
Similar questions
Q.
The function f (x) = x − [x], where [⋅] denotes the greatest integer function is
(a) continuous everywhere
(b) continuous at integer points only
(c) continuous at non-integer points only
(d) differentiable everywhere
Q.
The function f (x) = |cos x| is
(a) everywhere continuous and differentiable
(b) everywhere continuous but not differentiable at (2n + 1) π/2, n ∈ Z
(c) neither continuous nor differentiable at (2n + 1) π/2, n ∈ Z
(d) none of these
Q.
If
f
x
=
1
-
cos
x
x
sin
x
,
x
≠
0
1
2
,
x
=
0
then at x = 0, f (x) is
(a) continuous and differentiable
(b) differentiable but not continuous
(c) continuous but not differentiable
(d) neither continuous nor differentiable
Q.
Let
f
(
x
)
=
tan
(
π
[
x
−
π
]
)
1
+
[
x
]
2
, where
[
.
]
denotes the greatest integer function. Then
Q.
Let
f
:
R
→
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be a function such that
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(
x
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|
≤
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∈
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=
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f
is
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