Edexcel International GCSE Mathematics A · 4MA1
Differentiation
Differentiation gives a function’s rate of change. On a graph, the derivative gives the gradient of the tangent at a chosen x-value. A stationary point has zero derivative, but its y-coordinate still comes from the original function.
Key method
For a power term axⁿ, the derivative is anxⁿ⁻¹. Differentiate each term separately; a constant contributes zero.
Worked example
Find the stationary point of y = x² − 6x + 11.
- Differentiate: dy/dx = 2x − 6.
- Set the derivative to zero: 2x − 6 = 0, so x = 3.
- Substitute into the original function: y = 9 − 18 + 11 = 2.
Answer and interpretation
(3, 2), a minimum because the quadratic opens upwards.
Common mistake
Substituting x = 3 into the derivative gives the gradient, not the point’s y-coordinate.
Practise independently
Find the tangent gradient to y = 2x³ − x at x = 2.
Check your answer
dy/dx = 6x² − 1; at x = 2 the gradient is 23.
Syllabus connection
This lesson develops differentiation within the graphs and coordinate geometry area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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