Truning points and points of inflexion and max and min?

Question

f(x)=1/((x-1)(x-2))

please draw the graph

Answer 1

critical points when derivative = 0

Notice there are asymptotes when x = 1 and when x = 2

Just for easy i will expand the denominator

f(x) = 1/(x^2 - 3x + 2)

= (x^2 - 3x + 2)^(-1)

f ' (x) = -(2x - 3)(x^2 - 3x + 2)^(-2)

= -(2x - 3) / (x^2 - 3x + 2)^2 = 0

2x - 3 = 0

2x = 3

x = 3/2 = 1.5 is only critical point

which is half way between the 2 asymptotes

f (1.4) = -4.2

f(1.5) = -4

f(1.6) = -4.2

This is a local maximum

no points of inflection or local minimums