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: 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)