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Let f : (0 , pie) is defined to R by f(x) = max { sin2x, cos2x}. then show that the set of points of which f(x) has a local maxiam or minima is equlas to { pie/8 , pie/4 , 5 pie/8 } .
From the figure , the curve f(x) is shown in black bold line
the local minima is at : Pi/8 , 5Pi/8
and local maxima at : Pi/4
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period of cos2x,sin2x is pie
we will redefine the function given
now in(0,pie/8) cos2x.>sin2x , in (pie/8 to 5pie/8) sin2x>cos2x and in ( 5pie/8 to pie)again cos2x>sin2x (by comparing graph)
sof(x) = cos2x. (0,pie/8)
sin2x (pie/8 to 5pie/8)
cos2x ( 5pie/8 to pie)
now u can get it by drawing the graph
note : pie is not the answer because pie is the last point of the fonction so it is the global maxima not the local maxima.
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