If \(y = x^{3} – x^{2} – x + 6\), find the values of x at the turning point.
- \(\frac{1}{2}, 3\)
- \(\frac{1}{3}, -\frac{1}{2}\)
-
\(1, -\frac{1}{3}\)
- \(1, \frac{1}{3}\)
The correct answer is: C
Explanation
At turning point, \(\frac{\mathrm d y}{\mathrm d x} = 0\).
Given \(x^{3} - x^{2} - x + 6 \)
\(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 2x - 1 = 0 \)
\(3x^{2} - 3x + x - 1 = 0 \implies (3x + 1)(x - 1) = 0\)
\(x = \frac{-1}{3}, 1\)