f’(a) means the derivative of the function f, at the point a.

h and x-a= the distance between the the two point

$$ f'(a)=\lim_{x->a}\frac {f(x)-f(a)} {x-a} $$

We have two points, one (x, f(x)) one (a, f(a)) as x approaches towards a, even if x never reaches a, the slope of the secant line will yield out (approaching) the slope of the tangent line.

(one fix point and one variable point → a value i.e. definite slope.)

$$ f'(a)=\lim_{h->0} \frac{f(a+h)-f(a)} {h} $$

This is the same thing; h being the distance of point (a+h, f(a+h)) and point (a, f(a)), as h approaches to zero, the The two points of the secant line is approaching the given point for the tangent line, this means the slope of the secant line is approaching to the slope of the tangent line. (approaching) the slope of the tangent line.

(one fix point and one variable point → a value i.e. definite slope.)

$$ f'(a)=\lim_{h->0} \frac {f(x+h)-f(x)} {h} $$

This is the same thing; h being the distance of point (x+h, f(x+h)) and point (x, f(x)), as h approaches to zero, the The two points of the secant line is approaching the given point for the tangent line, this means the slope of the secant line is approaching to the slope of the tangent line.

(t variable point → a expression i.e. indefinite slope.)

If this limit exist, f(x) is said to be differentiable.