Question

The curve with equation y=8x^2+2/x has one turning point.

Find the coordinates of this turning point.

Answer 1

Coordinates of turning point is (½, 6)

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)