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NDA 2025 Maths · Mathematics · Continuity and Differentiability · medium

A function continuous on a closed interval [a,b] attains its maximum value on [a,b]. 2. A function continuous on an open interval (a,b) attains its…

Single correct option

Consider the following statements:
1. A function continuous on a closed interval [a,b][a,b] attains its maximum value on [a,b][a,b].
2. A function continuous on an open interval (a,b)(a,b) attains its maximum value on (a,b)(a,b).
Which of the statements given above is/are correct?
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
Show answer and solution

Answer: (A) 11 only

Statement 1 is the extreme value theorem: continuity on a closed bounded interval guarantees a maximum and a minimum. Statement 2 is false: f(x)=xf(x)=x is continuous on (0,1)(0,1) and takes values arbitrarily close to 11, but never reaches a largest value there.
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Original question written in the NDA 2025 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