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Question: The value of k for which f(x) = sinx – cosx – kx + b decreases for all real x is given by...

The value of k for which f(x) = sinx – cosx – kx + b

decreases for all real x is given by

A

k < 1

B

k ≥ 1

C

k≥2k \geq \sqrt{2}

D

k<2k < \sqrt{2}

Answer

k≥2k \geq \sqrt{2}

Explanation

Solution

Q f(x) is decreasing function

∴ f '(x) ≤ 0 ⇒ cos x + sinx – k ≤ 0

⇒ k ≥ cos x + sin x

Q cosx + sin x ∈ [−2,2]\lbrack - \sqrt{2},\sqrt{2}\rbrack

⇒ k ≥ 2\sqrt{2}