NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If f x = cos ⁡ x - 2 a x + b is a function which increases for all x , then the maximum value of 2 a + 1 is

Correct answer

Step-by-step solution

f x = cos x − 2 a x + b , f is differentiable everywhere. f ' x = − sin x − 2 a , f ' x ≥ 0 for all x ⇒ - sin x - 2 a ≥ 0 ⇒ sin x ≤ - 2 a f increases for all x ⇒ - 2 a ≥ 1 ⇒ 2 a + 1 ≤ 0 Hence, the maximum value of 2 a + 1 = 0

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