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II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. Slope = Derivative = The quantities, dy and dx are called “differentials”, and represent small, nonzero values for the changes in y and x. Specifically, if y=f(x), then Differentials are used to approximate changes in the output values of a function given small changes in the input values. THIS IS REALLY JUST THE SAME AS UTILIZING LINEAR APPROXIMATIONS, but allows us to shortcut the process of writing the equation of the line.

II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. Slope = Derivative = The quantities, dy and dx are called “differentials”, and represent small, nonzero values for the changes in y and x. Specifically, if y=f(x), then Differentials are used to approximate changes in the output values of a function given small changes in the input values. THIS IS REALLY JUST THE SAME AS UTILIZING LINEAR APPROXIMATIONS, but allows us to shortcut the process of writing the equation of the line.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Calculus I

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### II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. #### Slope = Derivative = The quantities, \(dy\) and \(dx\) are called "differentials", and represent small, nonzero values for the changes in \(y\) and \(x\). Specifically, if \(y = f(x)\), then Differentials are used to *approximate* changes in the output values of a function given small changes in the input values. **THIS IS REALLY JUST THE SAME AS UTILIZING LINEAR APPROXIMATIONS**, but allows us to shortcut the process of writing the equation of the line. **Picture:** (No specific graph or diagram is provided in the image. For a complete educational content, a diagram showing differentials on a curve might be necessary, typically representing a tangent line at a point on the function \(f(x)\), illustrating small changes \(dy\) and \(dx\) on the axes.)
Transcribed Image Text:### II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. #### Slope = Derivative = The quantities, \(dy\) and \(dx\) are called "differentials", and represent small, nonzero values for the changes in \(y\) and \(x\). Specifically, if \(y = f(x)\), then Differentials are used to *approximate* changes in the output values of a function given small changes in the input values. **THIS IS REALLY JUST THE SAME AS UTILIZING LINEAR APPROXIMATIONS**, but allows us to shortcut the process of writing the equation of the line. **Picture:** (No specific graph or diagram is provided in the image. For a complete educational content, a diagram showing differentials on a curve might be necessary, typically representing a tangent line at a point on the function \(f(x)\), illustrating small changes \(dy\) and \(dx\) on the axes.)
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