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NDA 2 2025 Maths, question 88

Topic: Differential calculus

Passage · Q87 to Q88

Let the function f(x)=∣x−3∣+∣x−4∣f(x)=|x-3|+|x-4| be defined on the interval [0,5][0,5].

Q88

Consider the following statements :

I. The function is differentiable at x=3x=3.

II. The function is differentiable at x=4x=4.

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 slopes are −2 for x<3, 0 for 3<x<4, and 2 for x>4.
  2. Left and right derivatives differ at both 3 and 4, so the function is differentiable at neither point.