Estimating Gradients (Edexcel IGCSE Maths A)

A tangent is a line that touches a curve at a point (and does not cross it).

The gradient of a curve at a point is defined to be the same as the gradient of the tangent to the curve at that point.

False.

Drawing a tangent line to a curve at a point will not always give the exact gradient of the curve at that point.

A tangent line is drawn by eye so it will give an estimate of the gradient.

Differentiation can be used to find the exact equation of the tangent.

To find an estimate for the gradient of a curve at a point:

• Draw a tangent to the curve at the point.

• Find the gradient of the tangent using

  • Gradient = rise ÷ run

  • or difference in y ÷ difference in x.

• The gradient of the tangent will give the estimate for the gradient of the curve at the point.