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NDA 2 2025 Maths, question 87

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].

Q87

What is dydx\frac{dy}{dx} at x=3.5x=3.5 equal to?

  1. (a) 00Correct answer
  2. (b) 11
  3. (c) 22
  4. (d) 3.53.5

Solution.

Answer: (a) 00

  1. For 3<x<4, f(x)=(x−3)+(4−x)=1, a constant.
  2. Therefore its derivative at 3.5 is zero.