Correct Answer: Option C

Explanation

f(x) = 2x\(^3\) - x\(^2\) - 4x – 4
f’(x) = 6x\(^2\) - 2x – 4
As f’(x) = 0
Implies 6x\(^2\) - 2x – 4 = 0
3x – x – 2 = 0 (By dividing by 2)
(3x + 2)(x - 1) = 0
3x + 2 = 0 implies x = \(\frac{-2}{3}\)
Or x - 1 = 0 implies x = 1
f’(x) = 6x\(^2\) - 2x – 4
f’’(x) = 12x – 2
At max point f’’(x) < 0
∴f’’(x) = 12x – 2 at x = 1
= 12(1) – 2
= 12 – 2 = 10
∴ Max at x = \(\frac{-2}{3}\)

There is an explanation video available below.

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