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NDA 1 2025 Maths, question 94

Topic: Differential calculus

Passage · Q93 to Q94

Let the function f(x)=x2+9f(x) = x^{2} + 9.

Q94

Consider the following statements:

I. f(x) is an increasing function.

II. f(x) has local maximum at x = 0.

Which of the statements given above is/are correct?

  1. (a) I only
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor IICorrect answer

Solution.

Answer: (d) Neither I nor II

  1. The derivative f′(x)=2xf\prime(x) = 2x is negative for x<0x < 0 and positive for x>0x > 0.
  2. Thus ff is not increasing on its full real domain, so I is false.
  3. Also f(x)=x2+9≥9=f(0)f(x) = x^{2} + 9 \geq 9 = f(0); zero is a local and global minimum, not a maximum.
  4. II is false.