Gradient of a Curve

Estimate the gradient of a curve by drawing a tangent to the curve

The steepness of a line is called its gradient.

A straight line has a constant gradient as the steepness doesn’t alter along the length of the line.

A line that slopes up to the right has a positive gradient.

The y-change is positive

A line that slopes down to the right has a negative gradient.

The y-change is negative.

Calculate the gradient of the line segment EF. 

Gradient = y-changes/x-changes

Gradients = -4/3

What is the gradient of this straight line?

Gradient = y-changes/x-changes

Gradients = 5/10=1/2

Some parts of this route have positive gradients but some have negative gradients.

​The gradient changes all the time.

​So if a line curves, it is because the gradient is changing.

This means that you cannot find the gradient of a whole curve but you are able to work out the gradient at any point along the curve.

By zooming in on a point, a line can be added that matches the slope of the curve

This line is called the tangent to the curve at that point.

Find the gradient at point C

Gradient = y-changes/x-changes

Gradient = 6/1=6

Find the gradient at point B

Gradient = y-changes/x-changes

Gradient = 4/-2=-2