f(x)=0.5*e^x(sinx+cosx)
对x求导,得
f'(x)=0.5*[e^x(sinx+cosx)+e^x(cosx-sinx)]
=0.5*e^x(2cosx)
在区间[0,π/2]上,cosx>0,e^x>0
∴f'(x)>0
∴在此区间上函数递增,
∴x=0时,函数取得最小值,最小值是f(0)=0.5
x=π/2时,函数取得最大值,最大值是f(π/2)=0.5*e^(π/2)*1=0.5*e^(π/2)
即函数f(x)在区间[0,π/2]上的值域是[0.5,0.5*e^(π/2)]
函数f(x)=0.5*e^x(sinx+cosx)在区间[0,π/2]上的值域
函数f(x)=0.5*e^x(sinx+cosx)在区间[0,π/2]上的值域
数学人气:238 ℃时间:2019-10-29 13:58:06
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