The GATE Grind

GATE 2018 CE (CE1) – Question 13

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice

At x = 0, $f(x)=x^3$ has ______.

  1. a local maximum
  2. a local minimum
  3. both a local maximum and minimum
  4. neither a local maximum nor a local minimum

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) neither a local maximum nor a local minimum

Explanation

The function $x^3$ is negative just left of 0 and positive just right of 0, remaining increasing through the stationary point. Thus 0 is a stationary inflection, with neither local maximum nor minimum (D).