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Byju's Answer
Standard XII
Mathematics
Proof of LaGrange's Mean Value theorem
The slope of ...
Question
The slope of the tangent to the curve x = 3t
2
+ 1, y = t
3
−1 at x = 1 is
(a) 1/2
(b) 0
(c) −2
(d) ∞
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Solution
(b) 0
Given
:
x
=
3
t
2
+
1
y
=
t
3
-
1
x
=
1
Now
,
3
t
2
+
1
=
1
⇒
3
t
2
=
0
⇒
t
=
0
d
x
d
t
=
6
t
and
d
y
d
t
=
3
t
2
∴
d
y
d
x
=
d
y
d
t
d
x
d
t
=
3
t
2
6
t
=
t
2
Thus
,
we
get
Slope of the tangent=
d
y
d
x
t
=
0
=
0
2
=0
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0
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Proof of LaGrange's Mean Value theorem
Standard XII Mathematics
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