CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=2 x^3+3 x^2-12 x+1\) is strictly increasing in :
- A [-2,1]
- B \((-\infty,-2] \cup[1, \infty)\)
- C \((-\infty, 1]\)
- D \((-\infty,-1] \cup[2, \infty)\)
Answer & Solution
Correct Answer
(B) \((-\infty,-2] \cup[1, \infty)\)
Step-by-step Solution
Detailed explanation
\(f'(x) = 6x^2+6x-12\) \(6x^2+6x-12 \ge 0\) \(x^2+x-2 \ge 0\) \((x+2)(x-1) \ge 0\) \(x \in (-\infty,-2] \cup [1,\infty)\)
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