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 ...
Using Log Graphs in Modelling What are log graphs? Log graphs are used when the scale of a graph increases or decreases exponentially It can very difficult to read specific values from graphs with ...
Using Exps & Logs in Modelling What is exponential modelling? Exponential modelling is where real-life situations are modelled using exponential growth and decay Exponential growth is typically...
Exponential Growth & Decay What are exponential growth and exponential decay? y = Aekt is exponential growth y = Ae-kt is exponential decay k > 0 so plus or minus sign in equation immediatel...
