Question

Find the largest region over which the function f is increasing or decreasing, for: f(x):(x-4)/(x+8)

f is increasing for x=

Answer 1

in general, a function f(x) is increasing when f ' (x) is positive, and is decreasing when f ' (x) is negative

so f '(x) = ( (x+8)(1) - (x-4)(1)/(x+8)^2
= 12/(x+8)^2

clearly 12/(x+8)^2 is always positive for all values of x , x ≠ -8
so the function is always increasing and never decreasing.

confirmation from my favourite website
http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x-4%29%2F%28x%2B8%29+%2C+-20+%3C+x+%3C+10

notice the vertical asymptote at x = -8