posted by Cheallaigh .
f(x)=((6x-3)/(x+6)) how do you find the intervals of decreasing and increasing...I found that there were no critical points yet I was also correct that the function increased (-I,-6) and (-6,I). I was wrong that there were no decreasing intervals though.
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
( 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)
If you don't know how to find first derivation
wolframalpha dot com
When page be open in rectangle type:
and click option =
When you see result click option:
If you want to see graph of your function in google type:
function graphs online
When you see list of results click on:
When page be open in blue rectacangle type:
Range x-axis from -100 to 100
Range y-axis from -100 to 100
Then click option :
You will see graph of your function.