CHAPTER 7

Differentiation in one and Several Variables. Applications to Optimization

7.1 Derivatives

The derivative of a real function at a point is the instantaneous rate of change of that function in a neighborhood of the point; i.e., it is a measure of how the dependent variable changes as a result of a small change in the independent variable.

Geometrically, the derivative of a function at a point represents the gradient of the tangent to the function at the point. The origin of the idea of the derivative comes precisely from the attempt to draw the tangent line at a given point on a curve.

A function *f* (*x*) defined in a neighborhood of a point ...

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