Geometric interpretation of the derivative

Geometrically, the derivative of a function $$f(x)$$ at a given point is the slope of the tangent to $$f (x)$$ at the point $$a$$.

(See the figure to understand it).


The straight line forms a certain angle that we call $$\beta$$.

Obviously, this angle will be related to the slope of the straight line, which we have said to be the value of the derivative at the given point.

So we have $$$\tan\beta = f'(a)$$$