已知函数f(x)=/x-1/+/2x-1/+/3x-1/+.+/100x-1/,则当x=___时f(x)取得最小值.
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![已知函数f(x)=/x-1/+/2x-1/+/3x-1/+.+/100x-1/,则当x=___时f(x)取得最小值.](/uploads/image/z/8578446-6-6.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%2Fx-1%2F%2B%2F2x-1%2F%2B%2F3x-1%2F%2B.%2B%2F100x-1%2F%2C%E5%88%99%E5%BD%93x%3D___%E6%97%B6f%28x%29%E5%8F%96%E5%BE%97%E6%9C%80%E5%B0%8F%E5%80%BC.)
已知函数f(x)=/x-1/+/2x-1/+/3x-1/+.+/100x-1/,则当x=___时f(x)取得最小值.
已知函数f(x)=/x-1/+/2x-1/+/3x-1/+.+/100x-1/,则当x=___时f(x)取得最小值.
已知函数f(x)=/x-1/+/2x-1/+/3x-1/+.+/100x-1/,则当x=___时f(x)取得最小值.
因为 |x-1|>=0 |2x-1|>=0 ...
所以
x = 0 时
f(x) = 1+1+1+...+1
= 100
最小.
我只知道,这个值肯定在1/100到1之间
应该酌情考量,我再想想……
解1)x<=1/100
f(x)=100-100*101/2*x=100-5050x
f(x)的最小值是x=1/100时f(1/100)=49.5
2)x>=1
f(x)=5050x-100
f(x)的最小值是x=1时f(1)=4950
3)1/100
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解1)x<=1/100
f(x)=100-100*101/2*x=100-5050x
f(x)的最小值是x=1/100时f(1/100)=49.5
2)x>=1
f(x)=5050x-100
f(x)的最小值是x=1时f(1)=4950
3)1/100
f(x)=i-[i(i+1)/2]*x+[(i+1+100)(100-i)/2]*x-(100-i)
=2i-100+(5050-i-i^2)*x
令g(x)=2/x-100+(5050-1/x-1/x^2)*x=5050x+1/x-101
g'(x)=5050-1/x^2=0
x=1/√5050 时g(x)取极小值2√5050 -101
因此i=[1/x]=71时f(x)取最小值2920/71
综合1)2)3)
x=1/71时 f(x)取最小值2920/71
收起