Posted by Cheallaigh on Saturday, April 28, 2012 at 8:11pm.
If fŒ(x) > 0 at each point in an interval I, then the function is said to be increasing on I.
fŒ(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
In your case :
fŒ(x) = 39 /( x + 6 ) ^ 2
39 positive
( x + 6 ) ^ 2 always positive except
when x = - 6
In point x = - 6 function has vertical asymptote
So function :
f( x ) = ( 6 x - 3 ) / ( x + 6)
always increasing
P.S.
If you don't know how to find first derivation
Go on:
wolframalpha dot com
When page be open in rectangle type:
derivative (6x-3)/(x+6)
and click option =
When you see result click option:
Show steps
If you want to see graph of your function in google type:
function graphs online
When you see list of results click on:
rechneronline.de/function-graphs
When page be open in blue rectacangle type:
(6x-3)/(x+6)
Set :
Range x-axis from -100 to 100
Range y-axis from -100 to 100
Then click option :
Draw
You will see graph of your function.