Torricili extended this work to other curves such as cycloid and then the formula was generalized to fractional and negative powers by Wallis in In an treatise, fermat is credited with an ingenious trick for evaluating the integral of any power function directly. Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which influenced further work in quadrature.
The first full proof of fundamental theorem of calculus was given by Isaac barrow. Newton and Leibniz building on this work independently developed the surrounding theory of infinitesimal calculus in the late 17 century. Also, leibniz did a great deal of work with developing consistent and useful notation and concepts. Newton provided some of the most important applications to physics, especially of integral calculus. Became a popular term for a field of mathematics based upon their insight.
Leibniz introduced the symbol for the integral and wrote the derivative of a function y of the variable x as both of which are still in use today. Format: ms-word doc Pages: 78 Chapter 1 to 4 With reference. 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 four contains the application of differentiation, summary and conclusion 1. It will state the fundamental of calculus, it shall also deal with limit and continuity. Finally, the goal of this work is to review the application of differentiation in calculus. Pioneers of modern calculus In the 17 th century, European mathematicians Isaac barrow, Rene Descartes, Pierre deferment the idea of a deferment. It also offers teachers' perspectives, and analyzes curriculum differentiation from a district or system perspective.
The authors challenge notions that curriculum differentiation is a neutral, necessary response to individual differences, or that it has an adverse impact on students.
Professional educators interested in understanding and improving the means by which high schools carry out the nearly impossible mandate of equitably distributing "humanized" knowledge while accommodating diversity will find this book an important resource. Home Curriculum Differentiation. Differentiation in Practice Author : Carol A. Lecture Notes on Differentiation A tangent line to a function at a point is the line that best approximates the function at that point better than any other line.
The slope of the function at a given point is the slope of the tangent line to the function at that point. The function f x is differentiable at a point x0 if f 0 x0 exists.
If a function is differentiable at all points in its domain i. The derivative of f that we have been talking about is called the first derivative. Theorem Extreme values local or global occur only at critical points and endpoints. Examples: 1. The following is the graph of f x. The function f x is concave up on the interval a, b if f 0 x is increasing on a, b.
The function f x is concave down on the interval a, b if f 0 x is increasing on a, b. The inflection point or point of inflection of a function f is defined to be the point at which the concavity changes. Notice the tangent lines and their slopes. A point of inflection is also labeled on the picture. Note: To find the inflection points, we look at the second derivative. Find all the points such that f 00 is zero or undefined at those points. Then use the Key Number Method to test the sign changes of f 00 at those points.
Therefore, At a production level yielding maximum profit, marginal revenue equals marginal cost.
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