CUET · MATHS · PYQ PAPER 2025
Consider the function \(f(x)=x^3-3 x\). Then Match List-I with List-II:
| List-I | List-II |
| (A) Point of local Maxima | (I) 1 |
| (B) Point of local Minima | (II) -1 |
| (C) Local maximum value | (III) 2 |
| (D) Local minimum value | (IV) - 2 |
- A (A) - (II), (B) - (I), (C) - (III), (D) - (IV)
- B (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
- C (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
- D (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
Answer & Solution
Correct Answer
(A) (A) - (II), (B) - (I), (C) - (III), (D) - (IV)
Step-by-step Solution
Detailed explanation
\(f'(x) = 3x^2 - 3\) \(3x^2 - 3 = 0 \implies x^2 = 1 \implies x = \pm 1\) \(f''(x) = 6x\) For \(x = -1\): \(f''(-1) = 6(-1) = -6 For \(x = 1\): \(f''(1) = 6(1) = 6 > 0\). Thus, \(x = 1\) is a point of local minima. Local maximum value:…
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