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A particle moves along the curve 6y x3 plus 2Find the points on the curve at which they y-coordinates id changing 8 times as fast as the x-coordinates?
We have
6y=x3+2
y=x3/6+2/6
dy/dx=3x2/6+0=x2/2
We are interseted in finding the points for which the y-coordinate changes 8 times as the x-coordinates,so let
dy/dx=8
(2)=> x2/2=8
=>x2=16
=>x=+- 4
x=4=>y=4(3)/6+1/3=64/6+1/3=66/6=11
x=-4=>y=-4 (3)/6+1/3=-64/6+1/3=-62/6=-31/3
.
. . The reqd points are (4,11), (-4,-31/3)
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