Drag the red point in the display below to move the tangent line along the quartic (fourth order) curve.
You can see that the gradient function f'(x) of a quartic curve is a cubic curve.
Finally you can investigate higher order curves. In each case, the gradient function f'(x) will be a curve of one order lower.
| Select polynomial order: |
Summary/Background
A note about graphic calculatorsA graphic calculator may not be allowed in your exam. However you can use one for revision. The TI-83, or similar model, can display graphs and their gradient function for you.
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To set this up, go to the Y= screen. Against Y1= enter a simple curve, 3x^2+1 for example. Against Y2= you should make the following selections: |  |
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- The function that gives the gradient at any point on a given curve is called the gradient function for that curve
- If the curve is given by y=f(x), then the gradient function is often denoted by f'(x).
- If f(x) is quadratic, then f'(x) is linear
- If f(x) is cubic, then f'(x) is quadratic
- If f(x) is quartic (fourth degree), then f'(x) is cubic
Software/Applets used on this page
This page uses JSXGraph.
JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.
This page also uses the MathJax system for displaying maths symbols.
JSXGraph is a cross-browser library for interactive geometry, function plotting, charting, and data visualization in a web browser. It is implemented completely in JavaScript, does not rely on any other library. It uses SVG and VML and is fully HTML5 compliant.
This page also uses the MathJax system for displaying maths symbols.
This question appears in the following syllabi:
| Syllabus | Module | Section | Topic | Exam Year |
|---|---|---|---|---|
| AP Calculus AB (USA) | 3 | Differentiation | Slope | - |
| AP Calculus BC (USA) | 3 | Differentiation | Slope | - |
| AQA A-Level (UK - Pre-2017) | C1 | Differentiation | Slope | - |
| AQA AS Maths 2017 | Pure Maths | Differentiation | Gradients | - |
| AQA AS/A2 Maths 2017 | Pure Maths | Differentiation | Gradients | - |
| CBSE XI (India) | Calculus | Limits and Derivatives | Definition of a derivative | - |
| CCEA A-Level (NI) | C1 | Differentiation | Slope | - |
| CIE A-Level (UK) | P1 | Differentiation | Slope | - |
| Edexcel A-Level (UK - Pre-2017) | C1 | Differentiation | Slope | - |
| Edexcel AS Maths 2017 | Pure Maths | Differentiation | Gradients | - |
| Edexcel AS/A2 Maths 2017 | Pure Maths | Differentiation | Gradients | - |
| I.B. Higher Level | 6 | Differentiation | Slope | - |
| I.B. Standard Level | 6 | Differentiation | Slope | - |
| Methods (UK) | M8 | Differentiation | Slope | - |
| I.B. (MSSL) | 7 | Differentiation | Slope | - |
| OCR A-Level (UK - Pre-2017) | C1 | Differentiation | Slope | - |
| OCR AS Maths 2017 | Pure Maths | Differentiation Basics | Gradients | - |
| OCR MEI AS Maths 2017 | Pure Maths | Differentiation Basics | Gradients | - |
| OCR-MEI A-Level (UK - Pre-2017) | C2 | Differentiation | Slope | - |
| Pre-U A-Level (UK) | 4 | Differentiation | Slope | - |
| Scottish (Highers + Advanced) | HM1 | Differentiation | Slope | - |
| Scottish Highers | M1 | Differentiation | Slope | - |
| Universal (all site questions) | D | Differentiation | Slope | - |
| WJEC A-Level (Wales) | C1 | Differentiation | Slope | - |