Rates of Change
So, gradient:
Average Rates of Change
To calculate the average rate of change of a curve:
Instantaneous Rates of Change
The instantaneous rate of change on a graph is the rate of change at a specific point.
Without (advanced) calculus, you cannot calculate the rate of change. However, you can estimate it by finding the gradient of the tangent at a specific point of a curve.
Tip
The tangent is a straight line that touches the curve at only one point.
Derivative
The derivative function (also known as the gradient function) is the function that allows us to find the gradient of any point at a curve. This will be explored later on 6.02 - Differentiation from First Principles.
For example, the derivative function ( or ) of is .
As for has a negative rate of change (gradient), so does .