Question

y = x^2 − 9x + 29/x − 5

relative maximum (x, y) =
relative minimum (x, y) =

Answer 1

y' = (x^2-10x+16)/(x-5)^2

y" = 18/(x-5)^3

So, max/min if y'=0
max if y" < 0, min if y" > 0

The rest is just algebra.