# Differentiation From First Principles Explorer

- Author:
- Richard Trimble

## Explore

Use the p slider to reduce the size of the chord, each step shrinks the horizontal distance by a factor of ten.
What do you notice about the value of the gradient chord m?
Try other base points A

## Task 1

Using the chord approximation to the tangent write down the gradient of the tangent to at the following points: (1,1) (2,4) (3,9) Do you notice any relationships between the co-ordinates of the point and your answers?

## Task 2

Try editing the function f(x) to be (HINT type x^3) Explore the value of the gradient at the points below but using the chord approximation to the tangent. (1,1) (2,8) (3,27) Do you notice a relationship between the co-ordinates of your point and your answer

## New Resources

- The RGB color cube
- Копие на Линейни неравенства.
- Images 1. Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th order segments(Variant2)
- Distance Formula Exploration
- Rhombicosidodecahedron (V=60) from Biscribed Pentakis Dodecahedron for the case of trisection of its 9th order segments(Variant2)