Hi,

Does anyone know how you work out the intervals on which a function is increasing or decreasing and any stationary points, local maxima and local minima?

The function I have is $\displaystyle f(x)=\frac{13-6x}{4-x^2}$

I have differentiated it and have $\displaystyle f '(x)=-\frac{6x^2-26x+24}{(4-x^2)^2}$

Which can be factorised to $\displaystyle \frac{2(-3x-4)(x-3)}{(2+x)(2-x)}$

From other eg's I think a sign table is the best way of doing this, but I'm not sure what the headings / columns should be.

From trial and error I know there is a stationary point at 3, i.e. f '(x) is 0 when x=3, but I'm not sure how to work out the other things.

I would be really grateful for any advice