If \(y = x^{3} - x^{2} - x + 6\), find the values of x at the turning point.

A.

\(\frac{1}{2}, 3\)

B.

\(\frac{1}{3}, -\frac{1}{2}\)

C.

\(1, -\frac{1}{3}\)

D.

\(1, \frac{1}{3}\)

Correct answer is C

At turning point, \(\frac{\mathrm d y}{\mathrm d x} = 0\).

Given \(x^{3} - x^{2} - x + 6 \)

\(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 2x - 1 = 0 \)

\(3x^{2} - 3x + x - 1 = 0 \implies (3x + 1)(x - 1) = 0\)

\(x = \frac{-1}{3}, 1\)