The GATE Grind

GATE 2014 EE (EE2) – Question 13

Engineering Mathematics · Calculus: Maxima and minima · 1 mark · Multiple choice

Where does real-valued $f(x)=(x-1)^{2/3}$ attain its minimum?

  1. $-\infty$
  2. $0$
  3. $1$
  4. $\infty$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $1$

Explanation

For real x,the expression is the square of the real cube root of x−1,so it is nonnegative. It is zero exactly when x−1=0. Consequently its global minimum occurs at **x=1,C**; differentiability at this cusp is unnecessary for locating the minimum.