Question

若|x|小于等于π/4,求函数f(x)=sin平方x+cosx的最小值

Answer 1

f(x)=(sinx)^2+cosx

=1-(cosx)^2+cosx

=-(cosx)^2+cosx+1

设t=cosx |x|≤π/4 √2/2≤t≤1

y=-t^2+t+1

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

在[√2/2,1]单调递减

取最小值时 t=1 y=1