Q.A particle moves along the curve `6y=x^3 + 2.` Find the points on curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

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The y coordinate changes 8 time faster than x coordinate. This means `(dy)/dx = 8` .

`6y = x^3+2`

By differentiation with respect to x;

`6(dy)/dx = 3x^2`

`6xx8 = 3x^2`

`x^2 = 16`

`x = +-4`

When `x = 4` then `y = 11`

When `y = -4` then `y = -31/3` .

*So there are two points where y coordinate changes 8 time faster than x coordinate.They are (4,11) and (-4,-31/3)*

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