maximum and minimum of a function

how would i find something like:

where and ...

where

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**here's what i did for ** where :

first we need critical points: so f'(x) = 0

so 1/2 - sin(x) = 0 , so

maxf(x) = max{f(0), f(pi/6), f(5/6pi), f(pi)}

f(0) = 1/2(0) + cos(0) = 1

f(pi/6) = 1/2(pi/6) + cos(pi/6) = pi/12 +

f(5/6pi) = 5/12pi + cos(5/6pi) = 5/12pi -

f(pi) = pi/2 - 1

so max is at f(pi/6) .. i.e pi/12 +

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now for where

critical points are again , but these both lie outside the range: so we only take into consideration -pi and 0:

so f(-pi) = -pi/2 - 1

f(0) = 1

so the max is at point f(0).. i.e 1..

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are these both correct? although seeming a bit obvious.. or do i need to show the final answer differently?