Question 1203551
The function at some point is different from the function at some point very very near to the function at that first point; this difference in function values is then divided by the small difference in the input values.  You are looking for the rate of change of a function.


What you want to do is let the "h" become increasingly small.  What is the result for   {{{(f(x+h)-f(x))/h}}} ?


Try that for your given function {{{f(x)=5x-2}}}.


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f(x)=5x-2


{{{f(x+h)=5(x+h)-2}}}


Subtracting that from f(x):
{{{5(x+h)-2-(5x-2)}}}
{{{5x+5h-2-5x+2}}}
{{{5x-5x+5h-2+2}}}
{{{5h}}}


This found difference is to be used, "over h", meaning h as a denominator:

{{{(5h)/h}}}
simplify this.
{{{5h/h=5cross(h)/cross(h)}}}
{{{highlight(5)}}}