3.5.3

Gradient of a Curve

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Gradient of a Curve

On a curved graph, the gradient at a point is the instantaneous rate of change.

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Tangent

  • The gradient of a curve at a point is the gradient of the tangent to the curve at that point.
  • The tangent is the line that just touches the curve at that point and lies parallel to the curve at that point.
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Average rate of change

  • The average rate of change can be calculated by drawing a line connecting two points on the curve.
  • This line is called a ‘chord’ of the curve and its gradient is an average of the rate of change between the two points.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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