- anonymous

I need help figuring out how the derivative of the graph would look approximatially.

- katieb

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- anonymous

|dw:1362964903781:dw|

- anonymous

This is the original graph how would the derivative look

- anonymous

rigth

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## More answers

- anonymous

so

- zepdrix

|dw:1362965404144:dw|These are the easy points to start with. Draw tangent lines. See how the slope of these tangent lines is 0. That means the VALUE of the derivative function will be zero.

- zepdrix

|dw:1362965478556:dw|

- anonymous

so then the derivative just goes along the x line

- zepdrix

No, the derivative passes through the x-axis at those 3 points :) now let's find some other points.

- anonymous

ok

- zepdrix

|dw:1362965586761:dw|Understand how I drew the line tangent to the curve?
See how it's pointing downward (read from left to right). It has an extremely negative slope. Meaning the derivative function will have an extremely negative VALUE at this x coordinate.

- zepdrix

|dw:1362965677365:dw|

- anonymous

ok

- anonymous

well then there you ave it

- zepdrix

|dw:1362965734778:dw|Now the function is starting to come together! c:

- zepdrix

Have you learned about inflection points? :o
Is this all too confusing farmergal? :c

- anonymous

no so then does it just go up to the x line then hit the dots on the x line.

- zepdrix

Yes, but it will keep going past the x line, how far? Well until we reach the inflection point.

- anonymous

Now I'm confussed when you say it keeps going to the inflection point.

- zepdrix

|dw:1362965901972:dw|Right around that point, it changes from `Concave Up` to `Concave Down`.

- anonymous

|dw:1362965979553:dw|SO it will look like this

- zepdrix

|dw:1362965980976:dw|

- zepdrix

Ummmm yah it looks like that's where we're headed :)

- anonymous

ok I got it so far.

- zepdrix

|dw:1362966105601:dw|

- anonymous

ok

- zepdrix

|dw:1362966148110:dw|So at that x coordinate, our derivative function reaches the bottom of the bowl :D

- anonymous

ok go it

- zepdrix

|dw:1362966245521:dw|If we check one last point way on the right over here, it appears to be very positive slope, so the derivative function will have a very positive value.

- zepdrix

|dw:1362966295539:dw|

- zepdrix

Something like that, the original graph was a tad sloppy. So it's hard to say for certain :) heh

- anonymous

ok got it thanks

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