What I'm doing is finding where this function is decreasing or increasing.
Here is the original function:
$f(x) = \ln(x+6)-2$
I take the prime when I believe is:
$f'(x)= \dfrac{1}{x+6}$
Then I made a sign chart.
I know right off the bat that there is nothing that make this function equal to zero because the numerator doesn't have an $x.$
The denominator can make the function undefined, and it's undefined at $-6.$ So thats the number I use on my sign chart.
I plugged the first value $-10$ into the prime function and it gives me a negative value:
$f'(-10)= \frac{1}{(-10+6)}$
$ = \frac{-1}{4}$
Then I plugged the $0$ in and I got
$f'(0)= 1/6$
It should look something like this:
- n | d +
-----(-10)------ ((-6)) -------(0)------
My homework is saying the function is never decreasing. >.