1.1.1 Derivatives

n high school you were introduced to one of the two main branches of calculus,

differential calculus. You saw that the derivative of a function y = f (x) at x = a is

defined by:

$f^{\prime}\left(a\right)=\lim_{h\to0}\frac{f\left(a+h\right)-f\left(a\right)}{h}$

or equivalently by

$f^{\prime}\left(a\right)=\lim_{x\to a}\frac{f\left(x\right)-f\left(a\right)}{x-a}$

When the limit exists, we say that f is differentiable at a