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

1. satellite73

you don't really need any calculus for this one

2. Xavier

Try factoring the numerator

3. satellite73

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

4. satellite73

it is always increasing

5. satellite73

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. satellite73

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

7. twirlere

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

8. twirlere

So what would the critical points be?

9. saloniiigupta95

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. twirlere

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

11. saloniiigupta95

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

12. twirlere

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

13. saloniiigupta95

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

14. twirlere

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

15. twirlere

I have to find the first derivative then factor