Question

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.

Answer 1

If fŒ(x) > 0 at each point in an interval I, then the function is said to be increasing on I.

fŒ(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.


In your case :

fŒ(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.