Estimating Gradients (Edexcel IGCSE Maths A)

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  • What is meant by a tangent to a graph?

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

  • What is meant by the gradient of a curve at a point?

    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.

  • True or False?

    Drawing a tangent line to a curve at a point will always give the exact gradient of 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.

  • How do you estimate the gradient of a curve at a point?

    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.