函数y=x3/2+(1-x)3/2,0
问题描述:
函数y=x3/2+(1-x)3/2,0
数学人气:988 ℃时间:2020-07-01 07:49:06
优质解答
y=x^(3/2)+(1-x)^(3/2)
y'=(3/2)x^(1/2)-(3/2)(1-x)^(1/2)
y'=0
x^(1/2)-(1-x)^(1/2)=0
x=(1-x)
x=1/2
xx>(1/2),y'>0
x=1/2,y最小值=2√(1/2)^3=1/(√2)
y'=(3/2)x^(1/2)-(3/2)(1-x)^(1/2)
y'=0
x^(1/2)-(1-x)^(1/2)=0
x=(1-x)
x=1/2
xx>(1/2),y'>0
x=1/2,y最小值=2√(1/2)^3=1/(√2)
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答
y=x^(3/2)+(1-x)^(3/2)
y'=(3/2)x^(1/2)-(3/2)(1-x)^(1/2)
y'=0
x^(1/2)-(1-x)^(1/2)=0
x=(1-x)
x=1/2
xx>(1/2),y'>0
x=1/2,y最小值=2√(1/2)^3=1/(√2)