Question 987858
{{{ (f(b)-f(a))/(b-a) }}} is used to find the <code>average rate of change</code> which is the slope of the <code>secant line</code> through the two points (a,f(a)) and (b,f(b))


{{{ (f(x+h)-f(x))/h }}} as a limit where h --> 0 is used to find the derivative f ' (x). The derivative function helps find the <code>instantaneous rate of change</code> which is the slope of the <code>tangent line</code> 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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