Question

how do i calculate the point on the curve when the ordinate changes 8 times faster than abscissa in the equation 6y=x^3+2

Answer 1

the conditions mean that the slope is 8.

y' is the slope, and since
6y' = 3x^2
y' = 1/2 x^2

If 1/2 x^2 = 8, then x = 4

So, at (4,11) the slope is 8

Answer 2

thank you