Show f(x) Is a Minimum

[nycmathguy]

David Cohen

How is this done? Seeking hints.

 

[MathLover1]

f(x)=(x-a)^2+(x-b)^2+(x-c)^2

show that f(x) will be a minimum when x is the avarage of a,b, and c

derivate

f(x)=2(x-a)+2(x-b)+2(x-c)..........equal to 0
0=2x-2a+2x-2b+2x-2c
2x+2x+2x-2a-2b-2c=0
6x-2(a+b+c)=0
6x=2(a+b+c)
x=2(a+b+c)/6
x=(a+b+c)/3 which the avarage of a,b, and c

 

[nycmathguy]

f(x)=(x-a)^2+(x-b)^2+(x-c)^2

show that f(x) will be a minimum when x is the avarage of a,b, and c

derivate

f(x)=2(x-a)+2(x-b)+2(x-c)..........equal to 0
0=2x-2a+2x-2b+2x-2c
2x+2x+2x-2a-2b-2c=0
6x-2(a+b+c)=0
6x=2(a+b+c)
x=2(a+b+c)/6
x=(a+b+c)/3 which the avarage of a,b, and c

Excellent. Nice job.