find the absolute extrema of the given function on the indicated interval f(x)=sin x+cos x, [pi/2, pi]

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The extreme values of the function f(x) = sin x + cos x are required for values of x that lie in the interval [pi/2, pi]

f'(x) = cos x - sin x

cos x - sin x = 0

=> cos x = sin x

This is true for x = pi/4 but pi/4 does not lie in the given interval.

In the given interval the graph is moving downwards uniformly.

Its highest value is 1 and the lowest value is -1

The extreme values of f(x) = sin x + cos x for x in [pi/2, pi] are 1 and -1

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