Homework Help: What would the first and second derivatives look like for this function?

1. Dec 4, 2011

agv567

1. The problem statement, all variables and given/known data

http://i.imgur.com/DQMRG.jpg

2. Relevant equations

The intervals are going by ones.

3. The attempt at a solution

Well for the first derivative, I'm guessing from -infinity to -1, it's a decreasing line?

Also from -1 to 1....it's a constant negative line? I dunno

2. Dec 4, 2011

Dick

I give up. What is the question?

3. Dec 4, 2011

agv567

Well the question was asking if the second derivative was increasing on its entire domain...

I think I'm sure this is what the first derivative looks like.

http://i.imgur.com/WSu1P.jpg

I'm having trouble graphing the Second though.

4. Dec 4, 2011

cepheid

Staff Emeritus

5. Dec 4, 2011

cepheid

Staff Emeritus
Remember that the first derivative is just the SLOPE of the curve you have there. For the first little bit, the slope appears to be nearly constant. Then it starts to decrease. Eventually the slope reaches 0. It continues to decrease and goes to some roughly constant negative value. Then it increases again and reaches 0. Etc. etc.

Once you have your curve for you first derivative, you can just repeat the same exercise again on IT to get a rough sketch of the second derivative.

6. Dec 4, 2011

agv567

Yeah thanks guys, I got it. The answer is TRUE by the way, The 2nd derivative is positive throughout,

7. Dec 4, 2011

Dick

Thanks for calling my attention the thread title, cepheid. But agv567, that's not right. And your blurry not very good sketch of the first derivative at least shows that it's sometimes decreasing and sometimes increasing. Doesn't that mean the the second derivative can't be positive everywhere?