Find the value of x for which the function f(x) = 2x

^{3}– x^{2}– 4x + 4 has a maximum value-
**A.**^{2}/_{3} -
**B.**

1 -
**C.**

–^{2}/_{3} -
**D.**

– 1

##### Correct Answer: Option B

##### 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 = –^{2}/_{3}

Or x + 1 = 0 implies x = -1

f’(x) = 6x^{2} – 2x – 4

f’’(x) = 12x – 2

At max point f’’(x)

∴f’’(x) = 12x – 2 at x = -1

= 12(-1) – 2

= -12 – 2 = -14

∴Max at x = 1