Since this is a calculus problem, I guess you need to know dy/dx at (1,√3/2).
Differentiate: 4x³=8x-8ydy/dx, so x³=2x-2ydy/dx. Now put x=1, y=√3/2:
1=2-(dy/dx)√3, (dy/dx)√3=1, dy/dx=1/√3 which is usually written √3/3 and corresponds to a slope of 30° to the x axis at the given point.