Wacth Ross Kemp On Gangs Oline

We see how y varies when x varies in a regular manner: the system more intuitively 'simple' to consider an interval on the y and the corresponding interval on the x and it the report: this will give me 'the average change. If you want the change to a point I'll have 'narrow ranges up to that point. Mathematically
: consider points xi axis
x0 and x0 + h, in their correspondence avro 'points
f (x0) and f (x0 + h) on the y axis
The distance between f (x0) and f (x0 + h) on the y axis (vertical) will be '
f (x0 + h) - f (x0)
while the distance between x and x0 the x axis will '
x0 + h - x0 = h
quotient call the ratio between the y-axis the distance along the x axis:

f (x0 + h) - f (x0)
------- ------------- = quotient
h

Now to get the derivative at the point x0 will be enough 'to tighten the interval by decreasing h

f (x0 + h) - f (x0)
Limhi-> 0 ----------------- = f '(x0) h



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Definition: derivative of a function is defined a point in the limit (if it exists and 'end) of the relationship of incremental approaches zero' h increase
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To have derived general will be enough 'to consider the point as x, that is' not fixed but generic x-axis