>.< help with anti derivatives graphically, and graphical origina function vs f`

Sparticl3

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>.< help with anti derivatives graphically, and graphical origina function vs f`

1] given the graph of the 1st derivative of a function, how do you sketch the graph of the original function?
I honestly just don't understand how to graph the anti-derivative... I understand that if i was given the original function to find the 1st derivative I would take the slopes of the tangent lines along given points on the functions graph. But when i am given just a tiny graph it is hard to estimate the slopes with any precision....


this book i have doesn't even come out and that we are graphically doing anti derivatives, it also just expects you to know random things like vertical transformations and there relation to the anti-derivative but they don't say anti-derivative anywhere in the text just the answers...


2] Also if given a graph with the three functions f, f`, and g (not the derivative of f) how can you tell which is which just from the graph and given no info about the equations of the functions? I am having problems doing this all graphically...I can do it ok with equations but graphically I am getting quite confused!
here is a link to a picture of the second problem

when I try too look at this graph it goes back to my confusion about the relationship btw the original function compared to the 1st derivative or vice versa....if it was the original function plus the 1st and second derivitves i feel likei could figure it out...but i dont even know what g is... i do know that g is used for anti deriviatives but i dont understand how we could separate the graph the anti derivative since it would be resting right on top of the original function so i do not know what g(x) is in this context

this link below is a picture i took of this problem out of my book !

http://imageshack.us/photo/my-images/171/clacproblem2.jpg/
 
1) The real trick is to gain a little confidence. You need a point on the anti-derivative. If one is not given, just pick one! When the derivative is positive, increase the value.
 
1) You understand how to construct a derivative from a graph. Good! The trick is to understand how to go the other way. It's testing your intuitive grasp of derivatives. It would be helpful to compare sample graphs with their derivatives: e.g. X2 and 2x or y=x and y=0. Notice where the slope is negative, zero and positive.

Does your book describe a method for doing this?

2) This problem again is testing the intuitive relation between a function and it's derivative. G is supposed to be an unrelated function.

Use the process of elimination. Is there a function that is zero slope at some point? What should the derivative be at the point?
 
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