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...
