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JAMB Mathematics 2007 Question 13

Question 13

Differentiation

Find the value of x for which the function f(x) = 2x3 − x2 − 4x + 4 has a maximum value.

  1. A.2/3
  2. B.1
  3. C.−2/3
  4. D.−1
Show the answer and explanation

Answer: C (−2/3)

Explanation

f'(x) = 6x2 − 2x − 4 = 2(3x + 2)(x − 1) = 0 at x = −2/3 or 1. f''(x) = 12x − 2 is negative at x = −2/3, so that is the maximum.