# stationary points question

• Jul 23rd 2010, 06:37 AM
porge111
stationary points question
"find the stationary points of the following curves and determine whether the points are maxima, minima, or points of inflexion"

y= (x + 1)/ (x - 1)

I know how to these sorts of questions but for this example i find it tricky, I set it as:

y= (x + 1) (x - 1)^-1 but then differentiating this is tricky - not sure how to use the chain rule on the latter, or the product rule overall.

thanks for any help.
• Jul 23rd 2010, 06:51 AM
earboth
Quote:

Originally Posted by porge111
"find the stationary points of the following curves and determine whether the points are maxima, minima, or points of inflexion"

y= (x + 1)/ (x - 1)

I know how to these sorts of questions but for this example i find it tricky, I set it as:

y= (x + 1) (x - 1)^-1 but then differentiating this is tricky - not sure how to use the chain rule on the latter, or the product rule overall.

thanks for any help.

In this case I would use the quotient rule:

$f(x) = \dfrac{u(x)}{v(x)}~\implies~f'(x)=\dfrac{v(x) \cdot u'(x) - u(x) \cdot v'(x)}{(v(x))^2}$

You should come out with: $f'(x)=-\dfrac2{(x-1)^2}$