video record
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The programme examines the use of the calculus for predicting and describing the behaviour of functions.
Metadata describing this Open University video programme
Module code and title: MS283, An introduction to calculus
Item code: MS283; 09
First transmission date: 06-11-1978
Published: 1978
Rights Statement: Rights owned or controlled by The Open University
Restrictions on use: This material can be used in accordance with The Open University conditions of use. A link to the conditions can be found at the bottom of all OU Digital Archive web pages.
Duration: 00:24:17
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Producer: Jean Nunn
Contributors: Louis Leithold; Graham Read
Publisher: BBC Open University
Keyword(s): Concave; Inflection
Footage description: Graham Read attempts to sketch the graph for the function f (x) = 3x4 + 2x3 by plotting only three points. He explains that there could be many other possibilities and uses a computer animation to show that this is so. Read goes on to explain why just plotting more points is not the answer to obtaining an accurate graph for a given function. He cites as an example the function f(x) = 10,000X / 10,000X-1. With the aid of computer animations and still graphics, Louis Leithold explains, in detail, the First Derivative Test which allows maxima and minima of functions to be determined and is therefore an aid in plotting accurate graphs of functions. Graham Read explains how the First Derivative Test is used in practise. With the aid of more computer animations and still graphics, Louis Leithold explains in detail the Second Derivative Test which allows points of inflection of a function to be located. Graham Read explains how to use the Second Derivative Test in practise. He then goes on to sum up the programme so far. Louis Leithold explains what the properties of the second derivative tell about the behaviour of the function. A computer animation helps to illustrate his points. Finally, Graham Read demonstrates, algebraically, the detailed use of the first and, second derivative tests with the function f (x) = 3x4 + 2x3. He sketches the graph of this function and compares it with a computer generated graph of the same function.
Master spool number: 6HT/73040
Production number: 00525_4318
Videofinder number: 457
Available to public: no