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

1. satellite73 Group Title

you don't really need any calculus for this one

2. Xavier Group Title

Try factoring the numerator

3. satellite73 Group Title

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

4. satellite73 Group Title

it is always increasing

5. satellite73 Group Title

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 Group Title

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

7. twirlere Group Title

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

8. twirlere Group Title

So what would the critical points be?

9. saloniiigupta95 Group Title

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 Group Title

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

11. saloniiigupta95 Group Title

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

12. twirlere Group Title

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

13. saloniiigupta95 Group Title

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

14. twirlere Group Title

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

15. twirlere Group Title

I have to find the first derivative then factor