2007
Mathematics
67ca00ce0c643c71d77dee1f
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: 1
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) < 0 ∴f’’(x) = 12x – 2 at x = -1 = 12(-1) – 2 = -12 – 2 = -14 ∴Max at x = 1
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) < 0 ∴f’’(x) = 12x – 2 at x = -1 = 12(-1) – 2 = -12 – 2 = -14 ∴Max at x = 1THIS WEEK's
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