Question

求大神指导.函数F(x)=cosx-sin^2x的最大值

Answer 1

F(x)=cosx-sin^2x

=cosx-(1-cos^2x)

=cosx-1+cos^2x

=cos^2x+cosx-1

=(cosx+1/2)^2-5/4

因为-1≤cosx≤1

对称轴为cosx=-1/2

所以最大值在cosx=1时取到

f(x)最大值=3/2^2-5/4=1