Question
Consider the following for the two (02) items that follow: Let f(x) = cases x^3, & x^2 What is _ x 0 f'(x) equal to?
NDA
Mathematics
Continuity and Differentiability
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 2
- B. 1
- C. 0
- D. Limit does not exist
Answer
C. 0
Step-by-step solution
Given f(x) = cases x^3, & x^2 For x 0, the relevant domain is x^2 In this interval, the function is f(x) = x^3. Differentiating with respect to x, we get: f'(x) = 3x^2 Taking the limit as x 0: _ x 0 f'(x) = _ x 0 3x^2 = 0 Answer: 0
Related: Mathematics — Continuity and Differentiability · All PYQ Banks