G1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate 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, including links to convex and concave sections and points of inflection.

Quick explanation

G1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate 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, including links to convex and concave sections and points of inflection

• This point belongs to Pure Mathematics, especially Derivative concept.
• You need to be able to g1 Understand and use the derivative of f(x) as the gradient of the tangent to y = f(x) at a general point; understand the gradient of the tangent as a limit and as a rate of change; sketch the gradient function for a given curve; understand second derivatives; differentiate 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, including links to convex and concave sections and points of inflection.
• The key ideas to know are gradient, tangent, and rate of change.
• Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.