Question

The value of a for which the function

f(x) = sin x – cosx –ax + b decreases for all real values of x is given by

• A. a ³$\sqrt{2}$
• B. a ³ 1
• C. a <$\sqrt{2}$
• D. a < 1

Answer 1

Answer: (A)

a ³$\sqrt{2}$

Answer 2

f ¢(x) = cos x + sin x – a £ 0

̃$\sqrt{2}$ sin (p/4 +x ) £ a

̃ sin (p/4 + x) £ a/$\sqrt{2}$

̃ $\frac{a}{\sqrt{2}}$³ 1 (Q sin (p/4 + x) £1)

̃ a ³$\sqrt{2}$