已知函数f(x)=根号2cos(2x-π/4)求f(x)在区间【-π/8,π/2】的最大值,最小值,并求出最值时x的值.

问题描述:

已知函数f(x)=根号2cos(2x-π/4)求f(x)在区间【-π/8,π/2】的最大值,最小值,并求出最值时x的值.

x∈[-π/8,π/2]则2x-π/4∈[-π/2,3π/4]当2x-π/4=0时,即x=π/8时,cos(2x-π/4)取得最大值1当2x-π/4=3π/4时,即x=π/2时,cos(2x-π/4)取得最小值-√2/2所以f(x)=√2cos(2x-π/4):在x=π/8时取得最大值,最大值为...