Q. 295.0( 1 Vote )

Find the interval

Answer :

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 .


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