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Unit 3 - Applications of Differentiation

 Derivatives have many mathematical applications. They can be used to find extrema, intervals of increasing/decreasing, inflection points, and concavity.Extrema are a fancy word for extreme values. This can either be minimum values (minima) or maximum values (maxima).Intervals of increasing/decreasing are the parts of a graph of a function in which it is going up or going down.Inflection points are points in which the concavity (bending) of a graph of function is changing. Concavity of a graph of a function can either be bending up (concave up) or bending down (concave down).Ultimately, the most important feature of differentiation is the optimization of a system. This deals with finding the most optimal constraints on a system.Unit 3 Inquiry ActivityUsing Derivatives to Find Limits3.A. L'Hospital's RuleBehavior of GraphsReal World Applications3.D. Physics of Basic Motion3.E. Related Rates - implicit differentiation in the real world3.F. Optimization - extrema in the real worldTheorems3.G. Mean Value TheoremNote: Many MVT problems are assessed based on implication of the theorem and are not explicit stated that MVT needs to be applied.Textbook ResourcesAnswer KeyRecommended Extra Practice Problems8.7 - page  #3.1 - page  #3.3 - page  #3.4 - page  #2.6 - page  #3.7 - page  #3.2 - page  #Free Response Questions (with solutions) Videos3.A. L'Hospital's RuleL'Hospital's Rule (conceptual and example problem)3.B. Increasing/Decreasing Intervals and Extrema & Critical Numbers3.C. Concavity and Inflection PointsConcavity and Inflection Points (conceptual)3.D. Physics of Basic Motioncoming soon...3.E. Related Rates3.F. Optimizationcoming soon...3.G. Mean Value Theorem