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Byju's Answer
Standard XII
Mathematics
Equation of Tangent at a Point (x,y) in Terms of f'(x)
A particle mo...
Question
A particle moves along the curve
6
y
=
x
3
+
2
. Find the points on the curve at which y - coordinate is changing 2 times as fast as x - coordinate.
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Solution
we need to find coordinates of point where
d
y
d
t
=
2
d
x
d
t
6
y
=
x
3
+
2
Differentiating on both sides
6
d
y
d
t
=
3
x
2
d
x
d
t
6
×
2
d
x
d
t
=
3
x
2
d
x
d
t
x
2
=
4
x
=
±
2
If
x
=
2
⇒
y
=
5
3
if
x
=
−
2
⇒
y
=
−
1
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