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Solution for Function F(X) = Cos X − 2 λ X is Monotonic Decreasing When (A) λ > 1/2 (B) λ < 1/2 (C) λ < 2 (D) λ > 2 - CBSE (Science) Class 12 - Mathematics

ConceptIncreasing and Decreasing Functions

Question

Function f(x) = cos x − 2 λ x is monotonic decreasing when
(a) λ > 1/2
(b) λ < 1/2
(c) λ < 2
(d) λ > 2

Solution

$f\left( x \right) = \cos x - 2 \lambda x$

$f'\left( x \right) = - \sin x - 2 \lambda$

$\text { For f(x) to be decreasing, we must have }$

$f'\left( x \right) < 0$

$\Rightarrow - \sin x - 2 \lambda < 0$

$\Rightarrow sin x + 2 \lambda > 0$

$\Rightarrow 2 \lambda > - \sin x$

$\text { We know that the maximum value of -sin x is 1 }.$

$\Rightarrow 2 \lambda > 1$

$\Rightarrow \lambda > \frac{1}{2}$

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Solution for question: Function F(X) = Cos X − 2 λ X is Monotonic Decreasing When (A) λ > 1/2 (B) λ < 1/2 (C) λ < 2 (D) λ > 2 concept: Increasing and Decreasing Functions. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science
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