Mathematics

Find the value of x for which the function f(x) = 2×3 – x2 -…

Find the value of x for which the function f(x) = 2x3 – x2 – 4x + 4 has a maximum value
  • A.2/3
  • B.
    1
  • C.
    2/3
  • D.
    – 1
Correct Answer: Option B
Explanation

f(x) = 2x3 – x2 – 4x – 4
f’(x) = 6x2 – 2x – 4
As f’(x) = 0
Implies 6x2 – 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) = 6x2 – 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