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.
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)