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

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