Question
For the following two (02) items: Let the function f(x) = |x - 3| + |x - 4| be defined on the interval [0, 5]. What is dy dx at x = 3.5 equal to?
NDA
Mathematics
Continuity and Differentiability
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 0
- B. 1
- C. 2
- D. 3.5
Answer
A. 0
Step-by-step solution
Given f(x) = |x - 3| + |x - 4| on the interval [0, 5]. At x = 3.5, we have 3 In the interval (3, 4), x - 3 > 0 and x - 4 Therefore, f(x) = (x - 3) - (x - 4) = 1. Since f(x) is a constant in the neighborhood of x = 3.5, its derivative is zero. dy dx = 0 at x = 3.5.
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