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NDA 2016 Maths · Mathematics · Application of Derivatives · medium

F(x)=x^3: 1. f has a local minimum at x=0. 2. f has a point of inflection at x=0.

Single correct option

Consider the following statements about f(x)=x3f(x)=x^3:
1. ff has a local minimum at x=0x=0.
2. ff has a point of inflection at x=0x=0.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

f′(x)=3x2≥0f'(x)=3x^2\ge0 with f′(0)=0f'(0)=0, so ff is increasing everywhere and has no local extremum; statement 1 is false. Since f′′(x)=6xf''(x)=6x changes sign at 00, the origin is a point of inflection, so statement 2 is true.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake