How is the average gradient between two points on a curve defined?
The expansion for a cubic term (x+h)3(x+h)^3(x+h)3 is x3+3x2h+3xh2+h3\boxed{x^3 + 3x^2h + 3xh^2 + h^3}x3+3x2h+3xh2+h3.
If f(x)=3x2f(x) = 3x^2f(x)=3x2, the simplified numerator f(x+h)−f(x)f(x+h) - f(x)f(x+h)−f(x) becomes 6xh+3h2\boxed{6xh + 3h^2}6xh+3h2.
The gradient of the chord (or secant) joining those two points.
Every term must contain a factor of hhh.
Flashcards for Edexcel A Level Maths 12.2 Differentiation from first principles, covering the key formulae, methods and definitions you need to recall for Paper 1, Paper 2 and Paper 3. 20 cards, matched to the Edexcel A Level Maths (9MA0) specification. Recall questions account for roughly 50% of marks at A Level Maths, so these target the marks you can secure before the paper starts.
