Answer:
Coordinates of turning point is (½, 6)
Step-by-step explanation:
We are given the equation of the curve as;
y = 8x² + (2/x)
At turning point, dy/dx = 0
Thus;
dy/dx = 16x - 2/x²
At dy/dx = 0, we have;
16x - 2/x² = 0
Rearrange to get;
16x = 2/x²
Multiply both sides by x² to get;
16x³ = 2
x³ = 2/16
x³ = 1/8
x = ∛(⅛)
x = ½
At x = ½, we have;
y = 8(½)² + (2/½) = 2 + 4 = 6
Thus, coordinates of turning point is (½, 6)
