NDA2026MathematicsApplication of DerivativesActual
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 ?
Options
- Ax 2 x 3
- Bx 3
- C(2,3)
- D[2,3]
Correct 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]