Consider the function `f(X)=(x^(2)-x+1)/(x^(2)+x+1)`
What is the maximum value of the fucnction ?

Options

A. `1//2`
B. `1//3`
C. 2
D. 3

Answer

D

Explanation

`f(x)=(x^(2)-x+1)/(x^(2))+x+1`
`f'(x)=((x^(2)+x+1)(2x-12)-(x^(2)-x+1)(2x+1))/(x^(2)+x+1)^(2)`
`=(2x^(2)-21)/(x^(2)+x+1)^(2)`
put f''(x)=0
`2x^(2)-2=0 `
f(x) is maximum at x=-1
f(-1)=3