Derivatives of function

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Can you suggest a function where this function has certain properties in its derivatives. The (4m+2)th derivative of this function has fixed sign in [ 0 , 3pi/4] and (4m+3)th , (4m+4)th derivatives have change sign in [ 0 , 3pi/4] , and (4m+5)th has fixed sign in [ 0 , 3pi/4] for all m where m is an integer number  we can change the interval.

Solution of the example in word.

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