The GATE Grind

GATE 2014 EE (EE2) – Question 38

Engineering Mathematics · Calculus: Maxima and minima · 2 marks · Multiple choice

Find the minimum of $x^3-3x^2-24x+100$ on [−3,3].

  1. 20
  2. 28
  3. 16
  4. 32

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 28

Explanation

The derivative is3x²−6x−24=3(x−4)(x+2),so only x=−2is a stationary point in the interval. Check it and both endpoints:f(−3)=118,f(−2)=128,f(3)=28. The smallest is **28,B**,at the right endpoint; the interior stationary point is a maximum.