Calculus- local/global max and min

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yahtzee

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f(x) = (8-x^2)e^-x

I have this function and I've already calculated the local min (at x= 4) and the local max value (at x= -2). The limit of this function is 0 when x-> infinity and -infinity when
x-> -infinity. The question is does this function assume any maximum or minimum value (aside from the local ones). Will the local min and max count as the global ones ?
I apologize if the question is unclear but am not sure how to explain what I mean.
 
yahtzee said:
f(x) = (8-x^2)e^-x

I have this function and I've already calculated the local min (at x= 4) and the local max value (at x= -2). The limit of this function is 0 when x-> infinity and -infinity when
x-> -infinity. The question is does this function assume any maximum or minimum value (aside from the local ones). Will the local min and max count as the global ones ?
I apologize if the question is unclear but am not sure how to explain what I mean.
Click to expand...
Plot the function using WolframAlfa and investigate.

What is the domain of the function?

Please come back and tell us what you found - then we can discuss further.
 
Last edited by a moderator:
Subhotosh Khan said:
Plot the function using WolframAlfa and investigate.
Click to expand...
No! Let the student graph the function by using the graphing techniques that they learned in class. This makes the student understand what is going on and enables them to really understand what is going on.

I have asked this question many times before but no one answers it so I will try again.

I do understand that we can (and probably should) allow students to use the new technology available. I do not have a problem with that but 1ST we need to figure out how to use this technology and still teach the students how to think mathematically. We just can't remove critical thinking from mathematics! You all know this! Until we figure out how to have thinking involved with mathematics while using the new technology we can't just use this technology in class. I liked learning how to curve sketch by hand as it put all the concepts together for me. Would I ever curve sketch by hand if I am near a computer? Absolutely not! Then again I know how to sketch a function by hand. If you did not get my question by now that I would like answered it is how can we use technology in the classroom but still teach students how to think?

I just made a post about a youtube channel I have that is all about understanding mathematics. How sad it would be if these proofs in my channel would be outdated one day. If they are then where will the new mathematicians come from? Just think about what you learned from reducing matrices. How can you really understand the later facts about matrices if you never reduced a matrix. To be honest, this scares the sh*t out of me.
 
Jomo said:
No! Let the student graph the function by using the graphing techniques that they learned in class. This makes the student understand what is going on and enables them to really understand what is going on.

I have asked this question many times before but no one answers it so I will try again.

I do understand that we can (and probably should) allow students to use the new technology available. I do not have a problem with that but 1ST we need to figure out how to use this technology and still teach the students how to think mathematically. We just can't remove critical thinking from mathematics! You all know this! Until we figure out how to have thinking involved with mathematics while using the new technology we can't just use this technology in class. I liked learning how to curve sketch by hand as it put all the concepts together for me. Would I ever curve sketch by hand if I am near a computer? Absolutely not! Then again I know how to sketch a function by hand. If you did not get my question by now that I would like answered it is how can we use technology in the classroom but still teach students how to think?

I just made a post about a youtube channel I have that is all about understanding mathematics. How sad it would be if these proofs in my channel would be outdated one day. If they are then where will the new mathematicians come from? Just think about what you learned from reducing matrices. How can you really understand the later facts about matrices if you never reduced a matrix. To be honest, this scares the sh*t out of me.
Click to expand...
Hmm interesting. Part of the question was to sketch the graph of the function and I have already done that:)
 
Honestly I was just wondering what counts as a global max/min and how to think about this. But the conclusion I've reached is that the global max is at x= -2 since f(x)->0 when x->infinity, and there is no global min since f(x)-> -infinity when x-> -infinity
 
Jomo said:
No! Let the student graph the function by using the graphing techniques that they learned in class. This makes the student understand what is going on and enables them to really understand what is going on.

I have asked this question many times before but no one answers it so I will try again.

I do understand that we can (and probably should) allow students to use the new technology available. I do not have a problem with that but 1ST we need to figure out how to use this technology and still teach the students how to think mathematically. We just can't remove critical thinking from mathematics! You all know this! Until we figure out how to have thinking involved with mathematics while using the new technology we can't just use this technology in class. I liked learning how to curve sketch by hand as it put all the concepts together for me. Would I ever curve sketch by hand if I am near a computer? Absolutely not! Then again I know how to sketch a function by hand. If you did not get my question by now that I would like answered it is how can we use technology in the classroom but still teach students how to think?

I just made a post about a youtube channel I have that is all about understanding mathematics. How sad it would be if these proofs in my channel would be outdated one day. If they are then where will the new mathematicians come from? Just think about what you learned from reducing matrices. How can you really understand the later facts about matrices if you never reduced a matrix. To be honest, this scares the sh*t out of me.
Click to expand...
Why not? I am not forbidding the student from using paper-pencil ( & eraser). I am "suggesting" the use of a tool that is quickly available to students - and just like "calculators" can be used by inquisitive students to their "great advantage". I think WA is an excellent tool - like using a straight-edge to draw line compared to "free-hand" drawing.
 
I know that I am nosed nosed about this topic but this is a math help forum after all.
Can you please respond to my question, please! and put this in a separate thread. I do not understand why no one wants to have a conversation about the point I am making in my question.
 
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