求y=√(x(20-x)(x-10)平方)的最值,x属于0~20

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 05:49:37
求y=√(x(20-x)(x-10)平方)的最值,x属于0~20

求y=√(x(20-x)(x-10)平方)的最值,x属于0~20
求y=√(x(20-x)(x-10)平方)的最值,x属于0~20

求y=√(x(20-x)(x-10)平方)的最值,x属于0~20
x(20-x)(x-10)^2
=(-x^2+20x)(x^2-20x+100)
=-(x^2-20x)(x^2-20x+100)
=-(x^2-20x)^2-100(x^2-20x)
=-[(x^2-20x)]-100(x^2-20x)-2500+2500
=-[(x^2-20x)+50]^2+2500
=-(x^2-20x+50)^2+2500
y=√[2500-(x^2-20x+50)^2]
=√{2500-[(x-10)^2-50]^2}
x属于[0,20]
x^2-20x=x(x-20)