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JAMB Mathematics 2011 Question 38

Question 38

Differentiation

Find the value of x at the minimum point of the curve y = x3 + x2 − x + 1.

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

Answer: A (1/3)

Explanation

dy/dx = 3x2 + 2x − 1 = (3x − 1)(x + 1) = 0 at x = 1/3 or −1. The second derivative 6x + 2 is positive at x = 1/3, so that is the minimum.