Stationary Points & Turning Points What are stationary points? A stationary point is any point on a curve where the gradient is zero To find stationary points of a function?f(x) Step 1:?Find th...
Second Order Derivatives What is the second order derivative of a function? If you differentiate the derivative of a function (ie differentiate the function a second time) you get the?second order ...
Increasing & Decreasing Functions What are increasing and decreasing functions? A function?f(x)?is?increasing?on an interval?[a,?b]?if?f'(x)?≥?0?for all values of?x?such that?a<?x?<?b. If...
Gradients, Tangents & Normals Using the derivative to find the gradient of a curve To find the gradient of a curve?y=?f(x)?at any point on the curve, substitute the?x?coordinate?of the point in...
Chain Rule What is the chain rule?? If?y?is a function of?u, and?u?is a function of?x, then the?chain rule?tells us that The chain rule allows us to differentiate more complicated expressions and?c...
Differentiating Powers of x How do I differentiate expressions involving powers of?x? Powers of?x?are differentiated according to the following formulae: Differentiating terms with positive integer...
Definition of Derivatives What is the derivative of a function?? Differentiation?is an operation that calculates the?rate of change?of a?function?with respect to a variable This means how much the ...
Definition of Gradient What is the gradient of a curve? At a given point the?gradient?of a curve is defined as the gradient of the?tangent?to the curve at that point A?tangent?to a curve is a line ...
Modelling with Sequences & Series What do I need to know about modelling with progressions? Many real-life situations can be modelled using progressions If a quantity is changing repeatedly by ...
Recurrence Relations What do I need to know about recurrence relations? A?recurrence relation?describes each term in a progression as a function of the previous term – ie?un+1?= f(un) Along with th...
Sigma Notation What is sigma notation? The symbol Σ is the capital Greek letter sigma – that's why it's called 'sigma notation'! 'Σ' stands for 'sum' – the expression to the right of the Σ tells yo...
Language of Sequences & Series What is a progression/sequence? A?progression?(or?sequence) is an?ordered?set of numbers with a rule for finding all the numbers in the progression The numbers in...
