Ready for Calculus

Everything in Foundations leads here. These articles explain the average rate of change, what a limit means and how to find one, and how the difference quotient turns into the derivative, the central idea of calculus.

Average Rate of Change and the Secant Line
The average rate of change of a function between $x = a$ and $x = b$ is the change in output divided by the change in input, $\frac{f(b) - f(a)}{b - a}$ . It is the slope of the secant line joining the two points.
What Is a Limit in Maths? Limits Explained for Beginners
A limit describes the value a function approaches as its input gets closer and closer to some number, whether or not the function is defined there. We write $\lim_{x \to a} f(x) = L$ .
What Is a Derivative? The Difference Quotient and the Slope of a Curve
The derivative of $f$ at $x$ is the slope of the curve at that point: the instantaneous rate of change. It is the limit of the difference quotient, $f'(x) = \lim_{h \to 0}\frac{f(x + h) - f(x)}{h}$ .