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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
is that the derivative?
ok set it to zero
Those are our critical points.
right now you can place them on a numberline
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|
To find that we use our derivative?
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.
at -1 it is increasing and at 1 it is decreasing it looks like this |dw:1449862096968:dw|
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
according to my calc they are both negative...
well at the points give the slopes are like this for my calculations: |dw:1449862387772:dw|
i plugged -2 and 2 into the derivative is that what i was supposed to do?
Thats what I did. its decreasing up to -1 and after 1. I can't tell between the two though
so what do i do next?
they both equal -3/25 when i plug in 2 and -2.......
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?