For y=f(x)y=f(x)y=f(x), the first derivative f′(x)f'(x)f′(x) gives the [ ] of the curve at each xxx.
- For x3x^3x3, f′′(x)=6xf''(x)=6xf′′(x)=6x changes sign.
- For x4x^4x4, f′′(x)=12x2f''(x)=12x^2f′′(x)=12x2 does not.
For y=f(x)y=f(x)y=f(x), the first derivative f′(x)f'(x)f′(x) gives the gradient of the curve at each xxx.
For a small change Δx\Delta xΔx, the change in gradient is approximately Δ(dydx)≈f′′(x)Δx\boxed{\Delta\left(\dfrac{dy}{dx}\right)\approx f''(x)\Delta x}Δ(dxdy)≈f′′(x)Δx.
Differentiate f′(x)f'(x)f′(x) with respect to xxx.
1.6.4 Differentiation Flashcards
Flashcards for CCEA A Level Maths 1.6.4 Differentiation, covering the key formulae, methods and definitions you need to recall for AS 1, AS 2, A2 1 and A2 2. 20 cards, matched to the CCEA A Level Maths (2210) 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.