Question

The function ƒ(x) = 1 + x (sin x) [cos x], 0 < x £p/2

• A. Is continuous on (0, p/2)
• B. Is strictly decreasing in (0, p/2)
• C. Is strictly increasing in (0, p/2)
• D. Has global maximum value 2

Answer 1

Answer: (A)

Is continuous on (0, p/2)

Answer 2

For 0 < x £ p/2, [cos x] = 0. Hence ƒ(x) = 1 for all x Î (0, p/2]. Trivially ƒ(x) is continuous on (0, p/2). This function is neither strictly increasing nor strictly decreasing and its global maximum is 1.