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A particle moves along the curve 6y = x...

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

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Here, it is given that `(dy/dt)/(dx/dt) = 8`
`=>dy/dx = 8`
Now, equation of curve, `6y = x^3+2`
`=> 6dy/dx = 3x^2`
`=> 2dy/dx = x^2`
`=>2**8 = x^2`
`=> x = +-4`
When `x = 4`,
`6y = 4^3+2 => y = 11`
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