1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
Value of c ...
Question
Value of
c
using Rolle's theorem for
f
(
x
)
=
{
x
2
+
1
,
when
0
≤
x
≤
1
3
−
x
,
when
1
<
x
≤
2
is:
A
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
−
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
does not exist
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is
D
does not exist
f
(
x
)
=
{
x
2
+
1
0
≤
x
≤
1
3
−
x
1
<
x
≤
2
f
1
(
x
)
=
{
2
x
0
≤
x
≤
1
−
1
1
<
x
≤
2
f
1
(
1
−
)
≠
f
1
(
1
+
)
L
⋅
H
⋅
S
≠
R
⋅
H
⋅
S
So
f
′
(
x
)
is not continuous.
∴
Rolle's theorem can't be applied.
Suggest Corrections
0
Similar questions
Q.
If
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
x
,
w
h
e
n
0
<
x
1
/
2
1
,
w
h
e
n
x
=
1
/
2
1
−
x
,
w
h
e
n
1
/
2
<
x
<
1
, then
Q.
Discuss the applicability of Rolle's theorem to the function
f
(
x
)
=
{
x
2
+
1
;
0
≤
x
<
1
3
−
x
;
1
<
x
≤
2
Q.
If
f
(
x
)
=
⎧
⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪
⎩
−
x
2
,
w
h
e
n
x
≤
0
5
x
−
4
,
w
h
e
n
0
<
x
≤
1
4
x
2
−
3
x
,
w
h
e
n
1
<
x
<
2
3
x
+
4
,
w
h
e
n
x
≥
2
,
The no. of values of
x
where
f
(
x
)
is not continuous is
Q.
Read the following statements.
Statement
1
:
Rolle's theorem holds for
f
(
x
)
=
|
sin
x
|
in
[
0
,
2
π
]
Statement
2
:
Rolle's theorem does not hold for
g
(
x
)
=
e
x
sin
x
in
[
0
,
π
]
which of the following option is correct.
Q.
Value of
′
c
′
of Rolle's Theorem for
f
(
x
)
=
{
x
2
+
1
,
0
≤
x
≤
1
3
−
x
,
1
<
x
≤
2
,for
x
∈
[
0
,
2
]
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Theorems for Differentiability
MATHEMATICS
Watch in App
Explore more
Theorems for Differentiability
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app