How Do You Determine the Derivative from a Graph?

[ussjt]

this is hard to explain because I can't post pictures of the two graphs, but I tried to draw them in paint. Here are the graphs: http://img.photobucket.com/albums/v629/ussjt/math.jpg

1)
the question asks estimate f '(0), f '(2), f '(5), f '(7)
when looking at at graph how do you determine the f '? I am confused about how to going about finding it.

2) at what points does the derivative exist? (how can you determine this?)
then sketch the derivative of s(the y-axis) (confused by the meaning)

Any help would be great.

 

[Jameson]

I cannot read your graphs on this post or another one you posted, but I'll try to help anyway. The derivative is simply the slope at that point, so you can easily tell if it's positive or negative. As long as you have slopes that are correct relative to each other, you should be fine.

The conditions for the existence of a derivative should be in your book, but if you see any "sharp turns" (like |x| graphs at x=0) then that's a no no. Other examples are cusps or any kind of discontinuity.

 

[mathmike]

when does the derivative exist? the derivative exists when the slope of your function is conntinous in other words when there are no assymtopes or points of discontinuity.
as far as looking at the graph to determine ther derivative just find the x value on the graph and determine if there is a discontinuity at that point

 

[ussjt]

http://img508.imageshack.us/my.php?image=math40wv.jpg

so for the second question, the derivatives are at the flat areas?

 

[Valhalla]

http://img508.imageshack.us/my.php?image=math40wv.jpg

so for the second question, the derivatives are at the flat areas?

No, the derivative does exist at flat areas. What is the derivative when the function is a horizontal line? What causes a derivative not to exist?? It was already mentioned in a reply.

 

[ussjt]

derivative when the function is a horizontal line is zero (right?) since it is a constant function. So the points that question 2 is asking for are the sharp turning points at the beginning and ends of the flat areas?