DIFFERENTIATION AND ITS APPLICATION
TABLE OF CONTENT
Table of content
Scope of the study and limitation
Purpose of the study
Significance of the study
Fundamental of calculus
Functions of a single variable and their graphs
Graph of a function
The rate of change of a function
Limits and continuity
Theory on limits
Infinite limits and limits at infinity Continuity
Differentiation as a limit of rate of change of elementary function
Gradient (straight line and curve)
Differentiation as a limit of rate of change of a function
Rules for differentiation
Differentiation of trigonometric function
Differentiation of a function of a function
Differentiation of implicit function
Differentiation of logarithmic, exponential and parametric function
Application of differentiation
The tangent and normal to a curve
Maxima and minima point
Point of inflexion
Summary and conclusion
This research is mainly on one aspect of calculus called differentiation and its application.
From the beginning of time man has been interested in the rate at which physical and non physical things change. Astronomers, physicists, chemists, engineers, business enterprises and industries strive to have accurate values of these parameters that change with time.
The mathematician therefore devotes his time to understudy the concepts of rate of change. Rate of change gave birth to an aspect of calculus know as DIFFERENTIATION.
There is another subject known as INTEGRATION.
Integration And Differentiation in broad sense together form subject called CALCULUS
Hence in a bid to give this research project an excellent work, which is of great utilitarian value to the students in science and social science, the research project is divided into four chapters, with each of these chapters broken up into sub units. Chapter one contains the introduction, scope of study, purpose of study, review of related literature and limitation.
Chapter two dwells on the fundamental of calculus which has to do with functions of single real variable and their graph, limits and continuity.
Chapter three deals properly with differentiation which also include gradient of a line and a curve, gradient function also called the derived function.
Chapter four contains the application of differentiation, summary and conclusion