Here's the question you clicked on:
twirlere
f(x)=(x^2-3x-4)/(x-2) Find points of increase and decrease and all relative extrema.
you don't really need any calculus for this one
Try factoring the numerator
it is a rational function with a slant asymptote at \(x-1\)
it is always increasing
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)
if you remember plotting rational functions in pre calc you may remember what something like this looks like
That's the derivative that I got also. I was trying to find the critical points from this...
So what would the critical points be?
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...
I can't factor \[x^2-4x-10\]
You are supposed to factor x^2 - 3x-4 ... I think your question says so...
Into... (x-2)(x-2)...?
x^2 - 3x - 4 =x^2 - 4x +x -4 = x(x-4) +1(x-4) = (x-4) (x+1)
And critical points are then x=4 and x=-1
I have to find the first derivative then factor