TheCalcHater
  • TheCalcHater
I need calculus help 2 questions.
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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TheCalcHater
  • TheCalcHater
here is the first one
1 Attachment
Kkutie7
  • Kkutie7
well you need to take the derivative to begin with. this will give you the slope which you can set to zero to see what your graph hits maximums and minimus
TheCalcHater
  • TheCalcHater
-x^2-1/(x^2+1)^2

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Kkutie7
  • Kkutie7
is that the derivative?
TheCalcHater
  • TheCalcHater
yes
Kkutie7
  • Kkutie7
ok set it to zero
TheCalcHater
  • TheCalcHater
x=1,-1
TheCalcHater
  • TheCalcHater
now what?
TheCalcHater
  • TheCalcHater
Those are our critical points.
Kkutie7
  • Kkutie7
right now you can place them on a numberline
TheCalcHater
  • TheCalcHater
|dw:1449861772893:dw|
Kkutie7
  • Kkutie7
aright now you want to check if the graph is increasing or decreasing between each critical point. Kind of like a limit |dw:1449861894332:dw|
TheCalcHater
  • TheCalcHater
To find that we use our derivative?
Kkutie7
  • Kkutie7
yeah you can use the derivative because it will give you either a positive or negative slope letting us know if its increasing or decreasing.
TheCalcHater
  • TheCalcHater
at -1 it is increasing and at 1 it is decreasing it looks like this |dw:1449862096968:dw|
Kkutie7
  • Kkutie7
you want to check up to the point like here check these points |dw:1449862205639:dw| plug them in and see if you get a negative or positive slope
TheCalcHater
  • TheCalcHater
according to my calc they are both negative...
Kkutie7
  • Kkutie7
well at the points give the slopes are like this for my calculations: |dw:1449862387772:dw|
TheCalcHater
  • TheCalcHater
i plugged -2 and 2 into the derivative is that what i was supposed to do?
Kkutie7
  • Kkutie7
Thats what I did. its decreasing up to -1 and after 1. I can't tell between the two though
TheCalcHater
  • TheCalcHater
oh ok.
TheCalcHater
  • TheCalcHater
so what do i do next?
TheCalcHater
  • TheCalcHater
they both equal -3/25 when i plug in 2 and -2.......
TheCalcHater
  • TheCalcHater
I found the derivative of - x^2-1/(x^2+1)^2. I then set it to zero to get x=1,-1 as our critical points. I then plugged in -2 and 2 into the derivative to see whether it has a negative or positive slope. The relative extrema is x=0 is the local max and x=sqrt3,-sqrt3 is a local minimum. Am i right?

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