UPSEE Solved Model Paper 5

since, f (x) = sin x - cos x - ax + b
∴ f ' (x) = cos x + sin x - a
Thus the function decreases if cos x + sin x - a ≤ 0 ⇒ cos x + sin x ≤ a
⇒ √2sin(x+

π

4

) ≤ a ⇒ √2 ≤ a
∴ The function decreases only is a ≥ √2