The value of $ k $ in order that $ f(x)=\sin x-\cos x-k x+b $ decreases for all real values is given by:

Question

The value of $ k $ in order that $ f(x)=\sin x-\cos x-k x+b $ decreases for all real values is given by:, $ k < 1 $, $ k>1 $, $ k>\sqrt{2} $, $ k < \sqrt{2} $

MARKS App · Accepted Answer

Given: ⇒ f x = sin x - cos x - k x + b ⇒ f ' x = cos x + sin x - k For decreasing function f ' x 0 So, cos x + sin x - k 0 The maximum value of cos x + sin x is 2 . ⇒ 2 - k 0 ⇒ k > 2

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