f(x)=x²-x+1÷x²+x+1 find minimum value of f(x)

f(x) =x²-x+1/x²+x+1 = (x²+x+1- 2x )/x²+x+1
Hence, f(x) = 1 - 2x/x²+x+1
df(x)/dx = 0
x = 1, -1
Now find the value of d/dx(df(x)/dx) at x = 1,-1
For x = +1, it is positive. Hence there is a minima at x = +1.
Therefore Minimum value of f(x) is at x=+1 which is f(+1) = 1/3

Approved

1/3