The curve C has the equation: 16y^3 +9x^2y-54x=0, find the x coordinates of the points on C where dy/dx = 0

C: 16y³ + 9x²y -54x = 0 d/dx(16y³) + d/dx(9x²y) + d/dx(-54x) = d/dx(0).............=>48y².dy/dx + 9x².dy/dx + y.18x - 54 = 0 dy/dx(48y²+9x²) = 54 - 18xy...........................................=> dy/dx = (54-18xy)/(48y²+9x²) = 0 # dy/dx=0 at turning points therefore: 54-18xy = 0 => y = 3/x # substitute y=3/x into C:=>16.(3/x)³ + 9x²(3/x) -54x = 0 = 432/x³ + 27x -54x = 0 = 432/x³ -27x = 0= 432/x³ = 27x = 432 = 27x⁴ = 6 = x⁴ ................................................=> x = 2, -2