Given:- Function f(x) = log sin x
Theorem:- Let f be a differentiable real function defined on an open interval (a, b).
(i) If f’(x) > 0 for all , then f(x) is increasing on (a, b)
(ii) If f’(x) < 0 for all , then f(x) is decreasing on (a, b)
Algorithm:-
(i) Obtain the function and put it equal to f(x)
(ii) Find f’(x)
(iii) Put f’(x) > 0 and solve this inequation.
For the value of x obtained in (ii) f(x) is increasing and for remaining points in its domain it is decreasing.
Here we have,
Taking different region from 0 to π
Thus f(x) is increasing in \(\big(0, \frac{\pi}{2} \big)\)
Thus f(x) is decreasing in \(\big(\frac{\pi}{2}, \pi \big)\)
