Question
Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is S equal to ?
NDA
Mathematics
Application of Derivatives
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. \ x 2\ \ x 3\
- B. \ x 3\
- C. (2,3)
- D. [2,3]
Answer
D. [2,3]
Step-by-step solution
Given f(x) = x^3 3 - 5x^2 2 + 6x + 7 Differentiating with respect to x, we get: f'(x) = x^2 - 5x + 6 f'(x) = (x - 2)(x - 3) For the function to be decreasing, f'(x) 0. (x - 2)(x - 3) 0 x [2, 3] Therefore, the set S where f(x) decreases is [2, 3]. Answer: [2,3]
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