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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

NDA 2021 · Mathematics · Application of Derivatives

Consider the following statements in respect of the function...

Consider the following statements in respect of the function f(x)=x+1xf(x)=x+\frac{1}{x} : 1. The local maximum value of f(x)f(x) is less than its local minimum value. 2. The local maximum value of f(x)f(x) occurs at x=1x=1. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

We have x+1x≤−2x+\frac{1}{x} \leq-2 or x+1x≥2x+\frac{1}{x} \geq 2 Hence Local minimum value of f(x)f(x) is 2 and Local maximum value g(x)g(x) is -2 Hence statement 1 is correct.
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