Posted by **Cheallaigh** on Saturday, April 28, 2012 at 8:11pm.

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.

- Engineering Calculus -
**Bosnian**, Saturday, April 28, 2012 at 9:47pm
If f(x) > 0 at each point in an interval I, then the function is said to be increasing on I.

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

In your case :

f(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.

## Answer This Question

## Related Questions

- Calculus - find the intervals where the function is increasing and the intervals...
- calculus-domain - Hello, I would greatly appreciate your input. I just need some...
- calculus - f(x)= - 2x^3 + 45x^2 -300x +9 There are 3 intervals (-inf,A], [A,B...
- Calculus - For y=(1/4)x^4-(2/3)x^3+(1/2)x^2-3, find the exact intervals on which...
- Calculus - Find the intervals on which the given function is increasing and ...
- Calculus - Consider the function f(x)=-2x^3+33x^2-108x+2. For this function, ...
- calculus - the graph (x^5-15*x^3 +10) is sketched without axes and not to scale...
- calculus - Please help!! *f(x)= x(x+6)^1/2 find two x intercepts. Then show that...
- calculus - 8. f(x)= - 2x^3 + 45x^2 -300x +9 There are 3 intervals (-inf,A], [A,B...
- Calculus - For the function below, determine the intervals of concavity: f(x)=...

More Related Questions