A-Level Maths (Edexcel)

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Paper 1 and Paper 2: Pure Mathematics Differentiation

Using the Second Derivative Examples

15:29 Understand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles for small positive integer powers of x and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection.
Spec (P1P2)7.1 (P1P2)7.3
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