Find the absolute maximum values of f on the givern interval

Question

f(x) = x / x²-x+9 , [0,9]

Answer 1

First we assume you mean y = x/(x^2-x+9)

the derivative by quotient rule is [(x^2 - x +9) - x(2x - 1)] / (x^2 - x +9)^2 =

[ x^2 - x + 9 - 2x^2 + x] / (x^2 - x + 9)^2 =

[ -x^2 + 9 ]/ (x^2 - x + 9)^2

-x^2 + 9 = 0

x^2 - 9 = 0

SO the critical values are +or-3

f(3) = 0.2 so the max occurs at (3, 0.2)

the endpoints are (0,0) and (9, 0.125)