Question 987858: Taking a class which is throwing formulas at me fast and I don't understand them.
Also, seeing ones that seem similar but are different for example, these two in particular:
 and 
What are they, how are both used? and how do they relate to each other?
Also, I am confused in class is points: (a,f(a)) and (b,f(b)) the same as (x1,y1) and (x2,y2) or something totally different?
Thank you
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! is used to find the average rate of change which is the slope of the secant line through the two points (a,f(a)) and (b,f(b))
as a limit where h --> 0 is used to find the derivative f ' (x). The derivative function helps find the instantaneous rate of change which is the slope of the tangent line at a given x value on the function curve.
Side Note: if b --> a or a --> b, then you can use the first expression as a limit to find the derivative or slope of the tangent line. So both forms are valid for the tangent line, but the first form is more used with secant lines.
Another Side Note: yes, (a,f(a)) and (b,f(b)) is the same as (x1,y1) and (x2,y2). This is where x1 = a, x2 = b, y1 = f(a), y2 = f(b)
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If you need more help, or if you have any questions about the problem, feel free to email me at jim_thompson5910@hotmail.com
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