Question

求函数y=—cos^2x-sinx+1的最大最小值,并求是的最大最小值时x的集合

Answer 1

y=—cos^2x-sinx+1=sin^2x-sinx=(sinx-1/2)^2-1/4

max:2 sinx=-1 x=2kπ-π/2

min:-1/4 sinx=1/2 x=2kπ+π/6或2kπ+5π/6