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

Question

anonymous · Answer

you don't really need any calculus for this one

anonymous · Answer

Try factoring the numerator

anonymous · Answer

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

anonymous · Answer

it is always increasing

anonymous · Answer

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)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

So what would the critical points be?

anonymous · Answer

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...

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

I have to find the first derivative then factor