CUET · MATHS · PYQ PAPER 2025
For the function \(f(x)=-2 x^3+3 x^2+36 x-10\), which of the following is/are true?
(A) \(f\) is increasing in \((-\infty,-2)\)
(B) \(f\) is increasing in \((-2,3)\)
(C) \(f\) is decreasing in \((-\infty,-2)\)
(D) \(f\) is decreasing in \((3, \infty)\)
Choose the correct answer from the options given below:
- A (B) and (D) only
- B (B), (C) and (D) only
- C (A) and (D) only
- D (B) only
Answer & Solution
Correct Answer
(B) (B), (C) and (D) only
Step-by-step Solution
Detailed explanation
\(f'(x) = -6x^2 + 6x + 36\) \(-6x^2 + 6x + 36 = 0 \implies x^2 - x - 6 = 0 \implies (x-3)(x+2) = 0 \implies x = -2, 3\) For \(x \in (-\infty, -2)\): \(f'(x) For \(x \in (-2, 3)\): \(f'(x) > 0\), so \(f\) is increasing. (B) is true. For \(x \in (3, \infty)\):…
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