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CUET · MATHS · PYQ PAPER 2025

The function \(f(x)=x^4-2 x^2\) is increasing on

  1. A \((-1,0) \cup(1, \infty)\)
  2. B \((-\infty,-1) \cup(0,1)\)
  3. C \((-\infty, \infty)\)
  4. D \((-\infty, 0) \cup(1, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((-1,0) \cup(1, \infty)\)

Step-by-step Solution

Detailed explanation

\(f'(x) = 4x^3 - 4x\) \(4x^3 - 4x > 0\) \(4x(x^2 - 1) > 0\) \(4x(x-1)(x+1) > 0\) Critical points: \(x = -1, 0, 1\) Sign analysis for \(f'(x)\): Interval \((-\infty, -1)\): \(f'(-2) = -24 Interval \((-1, 0)\): \(f'(-0.5) = 1.5 > 0\) Interval \((0, 1)\):…