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

  • Thread starter agv567
  • Start date
  • #1
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Homework Statement



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

Homework Equations



The intervals are going by ones.

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
 

Answers and Replies

  • #2
Dick
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I give up. What is the question?
 
  • #3
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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
cepheid
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I give up. What is the question?
It's in the thread title.
 
  • #5
cepheid
Staff Emeritus
Science Advisor
Gold Member
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Homework Statement



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

Homework Equations



The intervals are going by ones.

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
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
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Yeah thanks guys, I got it. The answer is TRUE by the way, The 2nd derivative is positive throughout,
 
  • #7
Dick
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Yeah thanks guys, I got it. The answer is TRUE by the way, The 2nd derivative is positive throughout,
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?
 

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