I have the function

finding increasing and decreasing.

I set the first derivative

and get

They create 3 intervals

1st interval

to

second interval

to

third interval

to

I plugin in values from in between these intervals into the first derivative and try to find where it is positive and where it is negative. The positive places are where the function is increasing and negatives are the places where it is decreasing. Right?

My results

are decreasing

are increasing

Next I set the second derivative as zero and undefined.

for this I can see i got a lot of intervals

and

1st interval

to

second interval

to

third interval

to

forth interval

to

Here I will have to do the same thing as I did when finding the increasing and decreasing but in this case negatives are concave down and positives are concave up.

So My results yield

are concave down

are concave up (as they are positive)

are my answers are correct? Is there a quick way to understand that from the graph? Does that has be from the original graph?