定义域：x≠kπ+π/2
f(x)=1+√2cos(2x-π/4)/cosx x∈[-π/4,π/2]
f'(x)=[√2sinxcos(2x-π/4)-2√2sin(2x-π/4)cosx]/(cosx )^2
√2sinxcos(2x-π/4)-2√2sin(2x-π/4)cosx=0
x=π/4
f(-π/4)=0 f(π/4)=1+√2 f(π/2)-->-∞
∴最大值1+√2,无最小值.