Find the intervals in which the following function is :

(a) strictly increasing

(b)strictly decreasing

f(x) = sinx + cosx, 0 ≤ x ≤ 2π

Given: f(x) = sinx + cosx

f’(x) = cosx – sinx

Now, for maxima or minima, f’(x) = 0

Therefore,

cosx – sinx = 0

sinx = cosx

Which gives us, as 0 ≤ x ≤ 2π

The points divides the interval 0 ≤ x ≤ 2π into three disjoint intervals, namely .

Now we will check the nature of f(x) in these intervals.

f’(x) > 0, if

Thus, f(x) is increasing in the intervals .

Also,

f’(x) < 0, if

Thus, f(x) is decreasing in .