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3: Continuous Functions

Last updated

Jun 11, 2024
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- 2.9: Extra Problems for Chapter 2
- 3.1: How to Set up a Problem

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3.1: How to Set up a Problem
The process of setting up a verbally presented problem, using examples from algebra and geometry.
3.2: Related Rates
The process of setting up a problem where we are given the rate of change of one quantity and wish to find the rate of change of another, involving implicit differentiation.
3.3: Limits
Definition of the limit of a real function of one variable. Applying limits to determine the slope of a function at a particular point.
3.4: Continuity
Definition of continuity of functions. The relationship between continuity and differentiability at a point on a function.
3.5: Maxima and Minima
Definition of the maxima and minima on an interval of a function. The Critical Point Theorem, and tests for identifying maxima and minima.
3.6: Maxima and Minima — Applications
Examples of applications for function maxima and minima, in the physical and social sciences.
3.7: Derivatives and Curve Sketching
How to sketch curves of functions using first and second derivatives. Formal definitions of directions of concavity and points of inflection.
3.8: Properties of Continuous Functions
Introduction to hyperintegers. Discussion of the Intermediate Value Theorem, Extreme Value Theorem, and Rolle's Theorem.
3.9: Extra Problems for Chapter 3

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