## anonymous 3 years ago f(x)=(x^2-3x-4)/(x-2) Find points of increase and decrease and all relative extrema.

1. anonymous

you don't really need any calculus for this one

2. anonymous

Try factoring the numerator

3. anonymous

it is a rational function with a slant asymptote at $$x-1$$

4. anonymous

it is always increasing

5. anonymous

you could take the derivative and get $\frac{x^2-4x+10}{(x-2)^2}$ but the denominator is never negative, and neither is the numerator ( you can check that it has no zeros)

6. anonymous

if you remember plotting rational functions in pre calc you may remember what something like this looks like

7. anonymous

That's the derivative that I got also. I was trying to find the critical points from this...

8. anonymous

So what would the critical points be?

9. anonymous

Factorise the Numerator... Can you??? Then the critical points for an expression like this... $(x-a)(x-b)/ (x-c)$ are a,b and c...

10. anonymous

I can't factor $x^2-4x-10$

11. anonymous

You are supposed to factor x^2 - 3x-4 ... I think your question says so...

12. anonymous

Into... (x-2)(x-2)...?

13. anonymous

x^2 - 3x - 4 =x^2 - 4x +x -4 = x(x-4) +1(x-4) = (x-4) (x+1)

14. anonymous

And critical points are then x=4 and x=-1

15. anonymous

I have to find the first derivative then factor