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