Question 21 of 82intermediate🔧 ApplyShort Answer4 marks
Show that the function given by f(x) = sin x is
(a)
increasing in (0, π/2)
Answer
The function f(x) = sin x is increasing in (0, π/2).
(b)
decreasing in (π/2, π)
Answer
The function f(x) = sin x is decreasing in (π/2, π).
(c)
neither increasing nor decreasing in (0, π)
Answer
The function f(x) = sin x is neither increasing nor decreasing in (0, π).
Explanation
This question tests the application of derivatives to determine the nature of trigonometric functions. The context provides similar examples with cos x and sin 3x, showing the standard method of finding f'(x) and analyzing its sign in different intervals.