Question

How do you find the critical points for `y = x/(x-1)^2`?

Answer 1

Critical points would be those at which either `dy/dx=0` or it does not exist.

`dy/dx=( (x-1)^2 -x.2(x-1))/(x-1)^4`

=`((x-1) -2x)/(x-1)^3`

= `-(x+1)/(x-1)^3`

`dy/dx` would be equal to zero at x= `-1` and it does not exist at x=1. The critical points are thus x=`-1` and 1