Calculus, stationary point and sketching the curve i just need help with a tiny question.
Im doing caculus and is told to find stationary point and sketch curve.
I have determined that there are no stationary points. How do i graph this?
The original question is y= (x-1)/ (x^2 -9)
Thanks Everyone for your help!
 A: You need to take the first derivative of the given function: $y= \dfrac{(x-1)}{(x^2 -9)}$ and then set $y' = 0$. I.e., solve for the value(s) of $x$ for which $y' = 0$. 
Using the quotient rule, we find that
$$y' = \dfrac {x^2 - 2x + 9}{(x^2 - 9)^2} = 0$$ There are no such values of $x$ for which $y' = 0 $. But $y'$ is also useful for determining where the function is increasing and or decreasing.
To graph the function, note where the function is undefined: you'll have asymptotes to help bound portions of your graph. Note in particular, where the denominator equals $0$. Typically, you'd also plot any/all stationary points, after determining whether they are local minimums, maximums, etc. You're correct, there are no such minimums or maximums with your function. But there asymptotes. There will be three separate curves to plot: one which "hugs" closely by the y-axis, and the other two hyperbolic in form.
Then you may want to plot a few other values, to help "fill in the gaps" of the graph.
Compare your sketch, then to the following:


