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JAMB Mathematics 2009 Question 39

Question 39

Differentiation

The distance travelled by a particle from a fixed point is given as s = (t3 − t2 − t + 5) cm. Find the minimum distance that the particle can cover from the fixed point.

  1. A.2.3 cm
  2. B.4.0 cm
  3. C.5.2 cm
  4. D.6.0 cm
Show the answer and explanation

Answer: B (4.0 cm)

Explanation

ds/dt = 3t2 − 2t − 1 = (3t + 1)(t − 1) = 0 at t = 1 (for t > 0), and the second derivative is positive there. s = 1 − 1 − 1 + 5 = 4.0 cm.