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

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Homework Help Overview

The discussion revolves around analyzing the first and second derivatives of a given function, as presented in a linked image. Participants are exploring the behavior of these derivatives across specified intervals.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants attempt to describe the first derivative's behavior, suggesting it is decreasing in certain intervals and constant in others. Some express uncertainty about their interpretations. There is also discussion regarding the second derivative and whether it is positive across the entire domain.

Discussion Status

The conversation includes various interpretations of the first and second derivatives, with some participants providing graphical representations. There is a mix of attempts to clarify the question and responses that indicate confusion about the original problem. Some guidance is offered regarding the relationship between the first and second derivatives, though explicit consensus on the interpretations is lacking.

Contextual Notes

Participants reference the intervals of the function and the nature of the derivatives, but there is a noted lack of clarity in the original question, leading to some confusion in the discussion.

agv567
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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
 
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I give up. What is the question?
 
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.
 
Dick said:
I give up. What is the question?

It's in the thread title.
 
agv567 said:

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.
 
Yeah thanks guys, I got it. The answer is TRUE by the way, The 2nd derivative is positive throughout,
 
agv567 said:
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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