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Applications of Differentiation III - Optimization, Newton’s Method and Differentials

 Topic Review on "Title": Definition of the distance of an object : Distance is the difference between the final and initial position of an object. Definition of the speed of an object: The speed of an object is the rate at which the distance changes in a given period of time. Instantaneous Speed: The speed at any time, assumed to be a time interval of zero. Acceleration: Acceleration is the rate at which speed changes in a given period of time. Optimization: Optimization is determining the combination of variables or factors that result in an extreme being produced. Newton’s Method: Newton’s Method is a strategy for approximating the zero of a function that uses the tangent line approximation of a point on a curve to iterate closer to a zero. Differential: Differential is format for expressing a derivative that has many practical applications.

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 "Title" Tutorial Summary : This tutorial discusses the optimization of functions, Newton’s Method and Differentials. The concept of motion as it relates to derivatives is covered in this tutorial. The rate of change principle is introduced to assist with the velocity and acceleration ideals. Optimization ideals are presented with the help of word problems. Newton’s Method is mentioned with the help of the definition of a tangent line approximation. Differentials are defined with examples and graphical representation of them. Newton’s method allow for the approximation of the value of zeros.

 Tutorial Features: Specific Tutorial Features: Graphical illustrations of Newton’s Method, Optimization ideals and Differentials. Motion is presented with physical and graphical representation of it in some of the example problems. Velocity and acceleration ideals are discussed as they related to the distance of an object. Series Features: Concept map showing inter-connections of new concepts in this tutorial and those previously introduced. Definition slides introduce terms as they are needed. Visual representation of concepts Animated examples—worked out step by step A concise summary is given at the conclusion of the tutorial.

 "Title" Topic List: `Motion Velocity and accelerationOptimization problemsNewton’s MethodDifferentials`

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