Question

Find the relative extrema, the domain and range, the x and y intercepts, the asymptotes, and the slope of f'(x) at x=12. f(x)=(2x^2-36)/(x^2-144)

Answer 1

This would be a perfect problem to work through in geogebra. :)

Answer 2

Take a derivative to find the extrema (set f'(x)=0) To find the slope at 12 plug it in to the derivative f'(12)=?. The x intercepts, set y=0, y intercepts set x=0. The asymptotes are where the denominator is zero or (x^2-144)=(x+12)(x-12). Take a limit as x->infty and -infty to find any horizontal/slant asymptotes. The domain is all real numbers that don't make it undefined (12 and -12 in this case) Since there is a horizontal asymptote, the range may be a bit tricky :P

Answer 3

its tedious

Answer 4

It is, but graphing it is nice. Because derivatives allow you to get quick sketches (most of the time). At least in 2-space they do.

Answer 5

you wouldnt get the total credit in an exam but you know what you have to do
good

Answer 6

well, we gotta throw out the cartesian plane then

Answer 7

Total credit? x.x

Answer 8

use a new geometry of units to measure the relationship between more than 3 variables

Answer 9

Here is the visual explanation of your problem. :) You should be able to graph most of this by hand using the methods malevolence described.