The extreme values of the function fx=1sinx+4+1cosx−4    where x∈R  :

f'x=0⇒-cosxsinx+42+-sinxcosx-42=0⇒cosxcosx-42+sinxsinx+42=0    ⇒cos3x+sin3x+8sin2x-cos2x+16cos x+sin x=0⇒cosx+sinx =0                            ⇒tanx=−1⇒x=3π/4  or  7π/4Global minimum x=2nπ+3π/4;Global maximum x=2nπ+7π/4M=48−2,m=2242+1