What is the gradient of a curve?
- At a given point the gradient of a curve is defined as the gradient of the tangent to the curve at that point
- A tangent to a curve is a line that just touches the curve at one point but doesn't cut the curve at that point
- A tangent may cut the curve somewhere else on the curve
- It is only possible to draw one tangent to a curve at any given point
- Note that unlike the gradient of a straight line, the gradient of a curve is constantly changing
- A tangent only exists at points where a curve is smooth.
- For example, there is no tangent (or gradient) at one of the 'corners' in a modulus function.