求y=√(x(20-x)(x-10)平方）的最值,x属于0~20_数学解答

求y=√(x(20-x)(x-10)平方）的最值,x属于0~20

人气：371 ℃　时间：2020-06-08 11:04:39

解答

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+2500y=√[2500-(x^2-20x+50)^2]=√{25...