AS Mathematics₇₃₅₆

Understand and use the derivative of $\mathrm{f}\left(\mathit{x}\right)$ as the gradient of the tangent to the graph of $\mathit{y}$ = $\mathrm{f}\left(\mathit{x}\right)$ at a general point ( $\mathit{x}\mathit{,}$ $\mathit{y}$ ); 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 $\mathit{x}$

Understand and use the second derivative as the rate of change of gradient.

Differentiate ${\mathit{x}}^{\mathit{n}}$ , for rational values of $\mathit{n}\mathsf{,}$ and related constant multiples, sums and differences.

Apply differentiation to find gradients, tangents and normals, maxima and minima and stationary points.

Identify where functions are increasing or decreasing.