Question 9 - CBSE Class 12 Sample Paper for 2026 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Question 9 A function 𝑓(𝑥)=10−𝑥−2𝑥^2 is increasing on the interval (A) (−∞,−1/4] (B) (−∞,1/4) (C) [−1/4,∞) (D) [−1/4,1/4]Calculating f’(𝒙) f(𝑥) = 10 – 𝑥 – 2𝑥2 f’(𝑥) = – 1 – 2 × 2𝑥 f’(𝑥) = −(1 + 4𝑥) Putting f’(𝒙) = 0 −1(1 + 4𝑥) = 0 1 + 4𝑥 = 0 4𝑥 = −1 𝒙 = (−𝟏)/𝟒 Plotting points on number line Hence, f is strictly decreasing for 𝒙 > (−𝟏)/𝟒 f is strictly increasing for x < (−𝟏)/𝟒 Since f is strictly increasing for x < (−𝟏)/𝟒 Therefore, f is increasing for x ≤ (−𝟏)/𝟒 We write f is increasing in (−∞,−1/4] So, the correct answer is (A)