函数f(x)=-2x2+4x-1,x属于[0,3]的最小值为m,最大值为M,求M-m
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![函数f(x)=-2x2+4x-1,x属于[0,3]的最小值为m,最大值为M,求M-m](/uploads/image/z/7638593-41-3.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3D-2x2%2B4x-1%2Cx%E5%B1%9E%E4%BA%8E%5B0%2C3%5D%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BAm%2C%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BAM%2C%E6%B1%82M-m)
函数f(x)=-2x2+4x-1,x属于[0,3]的最小值为m,最大值为M,求M-m
函数f(x)=-2x2+4x-1,x属于[0,3]的最小值为m,最大值为M,求M-m
函数f(x)=-2x2+4x-1,x属于[0,3]的最小值为m,最大值为M,求M-m
f(x)=-2x2+4x-1=-2(x-1)²+1
∴当x=1时有最大值M=1
当x=3时有最小值m=-7
∴M-m=8
8
f(x)=-2x^2+4x-1=1-2(x-1)^2
x<[0,3],(x-1)^2>=0,且(x-1)^2<=(3-1)^2=4
-8<=-2(x-1)^2<=0
-7<=1-2(x-1)^2<=1
即-7<=f(x)<=1
m=-7,M=1
M-m=8