求函数y=sin^4x+cos^4x,x(0,π/6)的最小值
问题描述:
求函数y=sin^4x+cos^4x,x(0,π/6)的最小值
答
y=sin^4x+cos^4x
=sin^4x+cos^4x+2sin^2xcos^2x-2sin^2xcos^2x
=(sin^2x+cos^2x)^2-2sin^2xcos^2x
=1-1/2sin^22x
=1-1/4(1-cos4x)
=3/4+cos4x
无最小值,端点取不到