Given: f(x) = sinx + cosx
f’(x) = cosx – sinx
Now, for maxima or minima, f’(x) = 0
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 .
f’(x) < 0, if
Thus, f(x) is decreasing in .
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