3: Continuous Functions
- Page ID
- 155810
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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.


