1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Proof of LaGrange's Mean Value theorem
1) #160;Fin...
Question
1
)
F
i
n
d
a
p
o
i
n
t
o
n
t
h
e
c
u
r
v
e
y
=
x
3
,
w
h
e
r
e
t
h
e
tan
g
e
n
t
t
o
t
h
e
c
u
r
v
e
i
s
p
a
r
a
l
l
e
l
t
o
t
h
e
c
h
o
r
d
j
o
i
n
i
n
g
t
h
e
p
o
i
n
t
s
(
1
,
1
)
a
n
d
(
3
,
27
)
2
)
F
i
n
d
a
p
o
i
n
t
o
n
t
h
e
c
u
r
v
e
y
=
x
3
-
3
x
,
w
h
e
r
e
t
h
e
tan
g
e
n
t
t
o
t
h
e
c
u
r
v
e
i
s
p
a
r
a
l
l
e
l
t
o
t
h
e
c
h
o
r
d
j
o
i
n
i
n
g
t
h
e
p
o
i
n
t
s
(
1
,
-
2
)
a
n
d
(
2
,
2
)
U
sin
g
L
a
g
r
a
n
g
e
s
m
e
a
n
v
a
l
u
e
t
h
e
o
r
e
m
Open in App
Solution
Dear Student,
L
a
n
g
r
a
n
g
e
s
m
e
a
n
v
a
l
u
e
t
h
e
o
r
e
m
s
t
a
t
e
s
t
h
a
t
i
)
w
h
e
n
f
(
x
)
i
s
a
c
o
n
t
i
n
o
u
s
a
n
d
d
i
f
e
r
e
n
t
i
a
b
l
e
f
u
n
c
t
i
o
n
b
e
t
w
e
e
n
[
a
,
b
]
i
i
)
t
h
e
n
t
h
e
r
e
e
x
i
s
t
s
c
∈
[
a
,
b
]
s
u
c
h
t
h
a
t
f
'
(
c
)
=
f
(
b
)
-
f
(
a
)
b
-
a
a
p
p
l
y
t
h
e
a
b
o
v
e
t
h
e
o
r
e
m
i
n
t
h
e
g
i
v
e
n
q
u
e
s
t
i
o
n
1
)
y
=
x
3
i
s
c
o
n
t
i
n
o
u
s
a
n
d
d
i
f
f
e
r
e
n
t
i
a
b
l
e
b
e
t
w
e
e
n
[
1
,
3
]
t
h
e
n
f
'
(
x
)
=
d
d
x
x
3
=
3
x
2
n
o
w
f
'
(
c
)
=
f
b
-
f
(
a
)
b
-
a
l
e
t
b
=
3
a
n
d
a
=
1
3
c
2
=
f
3
-
f
1
3
-
1
3
c
2
=
27
-
1
3
-
1
3
c
2
=
26
2
3
c
2
=
13
c
2
=
13
3
c
=
13
3
n
o
w
a
s
w
e
k
n
o
w
f
'
(
x
)
i
s
t
h
e
s
l
o
p
e
o
f
tan
g
e
n
t
t
o
t
h
e
c
u
r
v
e
y
=
x
3
sin
c
e
i
t
h
a
s
t
o
b
e
p
a
r
a
l
l
e
l
t
o
l
i
n
e
j
o
i
n
i
n
g
(
1
,
1
,
)
a
n
d
(
3
,
27
)
h
e
n
c
e
f
'
(
x
)
=
27
-
1
3
-
1
=
26
2
=
13
h
e
n
c
e
t
h
e
r
e
q
u
i
r
e
d
x
c
o
o
r
d
i
n
a
t
e
i
s
13
3
n
o
w
y
c
o
r
d
i
n
a
t
e
=
x
3
y
=
13
3
3
H
e
n
c
e
r
e
q
u
i
r
e
d
p
o
i
n
t
i
s
13
3
,
13
3
3
q
u
e
s
t
i
o
n
2
t
h
e
g
i
v
e
n
c
u
r
v
e
i
s
y
=
x
3
-
3
x
t
h
e
g
i
v
e
n
f
u
n
c
t
i
o
n
i
s
d
i
f
f
e
r
e
n
t
i
a
b
l
e
a
n
d
c
o
n
t
i
n
o
u
s
i
n
i
n
t
e
r
v
a
l
[
1
,
2
]
b
y
L
M
V
t
h
e
o
r
f
'
(
c
)
=
f
b
-
f
a
b
-
a
n
o
w
f
'
(
x
)
=
d
d
x
x
3
-
3
x
=
3
x
2
-
3
h
e
n
c
e
f
'
(
c
)
=
3
c
2
-
3
b
=
2
a
n
d
a
=
1
f
'
(
c
)
=
f
b
-
f
a
b
-
a
3
c
2
-
3
=
2
3
-
3
×
2
-
1
3
-
3
2
-
1
3
c
2
-
3
=
8
-
6
-
1
-
3
1
3
c
2
-
3
=
2
-
-
2
1
3
c
2
-
3
=
4
1
3
c
2
=
3
+
4
c
2
=
7
3
c
=
7
3
H
e
n
c
e
r
e
q
u
i
r
e
d
p
o
i
n
t
i
s
7
3
a
n
d
y
c
o
o
r
d
i
n
a
t
e
i
s
y
=
x
3
-
3
x
y
=
7
3
×
7
3
-
3
7
3
=
7
3
×
7
3
-
3
=
7
3
×
7
-
3
×
3
3
y
=
7
3
×
-
2
3
H
e
n
c
e
t
h
e
r
e
q
u
i
r
e
d
p
o
i
n
t
i
s
7
3
,
7
3
×
-
2
3
Regards,
Suggest Corrections
0
Similar questions
Q.
Find the points on the curve y = x
3
− 3x, where the tangent to the curve is parallel to the chord joining (1, −2) and (2, 2).
Q.
Find a point on the curve y = x
3
− 3x where the tangent is parallel to the chord joining (1, −2) and (2, 2).
Q.
Find a point on the curve y = x
3
+ 1 where the tangent is parallel to the chord joining (1, 2) and (3, 28).
Q.
A point on the curve
y
=
x
2
+
x
, where the tangent is parallel to the chord joining the points (0, 0) and (1, 2) is
.
Q.
Using LMV Theorem, find a point on the curve
y
=
(
x
−
3
)
2
, where the tangent is parallel to the chord joining
(
3
,
0
)
and
(
5
,
4
)
.
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
MATHEMATICS
Watch in App
Explore more
Proof of LaGrange's Mean Value theorem
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
AI Tutor
Textbooks
Question Papers
Install app
