函数最值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 15:19:27
![函数最值](/uploads/image/z/13199734-46-4.jpg?t=%E5%87%BD%E6%95%B0%E6%9C%80%E5%80%BC)
函数最值
函数最值
函数最值
解f(x)=1/4[1/x+36/(5-x)]
=1/4[1/x+36/(5-x)]×1
=1/4[1/x+36/(5-x)]×[x+(5-x)]/5
=1/20[1/x+36/(5-x)]×[x+(5-x)]
=1/20[1+36+(5-x)/x+36x/(5-x)]
=1/20[37+(5-x)/x+36x/(5-x)]
=37/20+1/20[(5-x)/x+36x/(5-x)]
≥37/20+1/20×2√(5-x)/x×36x/(5-x)
=37/20+12/20
=49/20
故函数的最小值为49/20。