Topic 12 0.0 / 5 ? MathematicsDifferentiationASEdexcel Created by: Jemma1494Created on: 06-06-21 18:19 Uses for differentiation Differentiation is used to find the gradient of curves at a point This method is much better than using a tangent 1 of 10 Finding the derivative For y = f(x) y = f’(x) is the derivative Also written as dy/dx 2 of 10 Differentiation rules If f(x) = x^n Then f’(x) = nx^n-1 If y = x^n Then dy/dx = nx^n-1 3 of 10 Differentiating quadratics Differentiating a quadratic gives a linear equation this makes it easy to find the gradient 4 of 10 Tangent A line parallel to a curve at a point 5 of 10 Normal A line at a point on a curve that is perpendicular to the tangent 6 of 10 Increasing and decreasing functions Increasing functions f’(x) ≥ 0 Decreasing functions f’(x) ≤ 0 7 of 10 Second order derivative f’’(x) or d^2y/dx^2 Repeat the process for differentiating twice 8 of 10 Stationary points Stationary points on curves can be found using differentiation as the gradient will = 0 9 of 10 Min / max points Min point d^2y/dx^2 > 0 Max point d^2y/dx^2 < 0 10 of 10
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