CUET · MATHS · PYQ PAPER 2025
The function \(f(x)=x^4-2 x^2\) is increasing on
- A \((-1,0) \cup(1, \infty)\)
- B \((-\infty,-1) \cup(0,1)\)
- C \((-\infty, \infty)\)
- D \((-\infty, 0) \cup(1, \infty)\)
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 \((0, 1)\):…
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