Question

Question #c9e4c

Answer 1

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

The domain is `D = RR-{2}`

`f'(x) = ((x)'(x-2) - x(x-2)')/(x-2)^2`

`f'(x) = (x-2-x)/(x-2)^2 = -2/(x-2)^2`

To find the local max an min of `f(x)`, you need to study the sign of the derivative :

You are absolutely right, there aren't any local max or min.

`f''(x) = ((-2)'(x-2)^2-(-2)((x-2)^2)')/(x-2)^4`

`f''(x) = (4(x-2))/(x-2)^4 = 4/(x-2)^3`

To find the intervals in which `f(x`) is concave up or concave down, you need to study the sign of the second derivative :

The function is concave down for `x in ]-oo;+2[` and is concave up for `x in ]+2;+oo[`.