Modelling with Differentiation inc. Optimisation How can I use differentiation to solve modelling questions? Derivatives can be calculated for any variables – not just y and x In every case the der...
Sketching Gradient Functions How can I sketch a function's gradient function? Using your knowledge of gradients and derivatives you can use the graph of a function to sketch the corresponding gradi...
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...
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...
First Principles Differentiation What is the derivative or gradient function? For a curve y = f(x) there is an associated function called the derivative or gradient function The derivative of f(x) ...
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 ...
