Calculus Tutorial 4

The derivative of a function f(x) is a new function f'(x) that outputs the slope of the tangent to f(x) at a given x-value.

If f'(x) exists for every x-value in the domain of f(x), then we say that f(x) is differentiable.

In this tutorial, we use limits to define f'(x), and we look at rules that can be used to find f'(x) when f(x) is a polynomial.

Finally, we prove that all differentiable functions are continuous, and we look at an example of a continuous function that is not differentiable.

* Aimed at students in their final two years of high school.

* Studying mathematics is best done by working through examples and exercises. There are many interactive examples and exercises in this tutorial that must be completed to achieve 100% progress.

* Written by a Maths teacher with 20 years of teaching experience.

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