Maths

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14 Terms

1
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Quadratic Formula of form ax2 + bx + c = 0

x = (-b +- √(b2 - 4ac))/2a

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First Derivative

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Arithmetic Growth Rate

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Logarithmic Growth Rate

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Locating Minima and Maxima of a Function

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Stationary Points

Minima and maxima are what we call stationary points  i.e., points of a function with a first derivative equal to zero z is a stationary point of f(x) if and only if:

<p>Minima and maxima are what we call stationary points&nbsp; i.e., points of a function with a first derivative equal to zero z is a stationary point of f(x) if and only if:</p>
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Inflection Points

a point where a function’s curvature shifts or, in mathematical terms, when a function’s second derivative equals zero z is an inflection point of f(x) if and only if:

<p>a point where a function’s curvature shifts or, in mathematical terms, when a function’s second derivative equals zero z is an inflection point of f(x) if and only if:</p>
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Global vs Local Optima

A function f(x) can have multiple minima and maxima 

  • global minimum (maximum) – smallest (greatest) value of f(x) importantly, in all its domain (global -> for all xs)

  • local minimum (maximum) – smallest (greatest) value of f(x) in an interval of its domain (local -> for a subset of xs only)

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Natural Logarithm Rule

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Rule on Exponentials of Base e

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Partial Derivatives

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Cross-Partial Derivatives

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Second Order Partial Derivatives

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Optimising Multivariate Functions

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