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- https://math.libretexts.org/Learning_Objects/GeoGebra_Simulations/Optimization%3A_Function_and_Rectangle_I_(GeoGebra)
- https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Yet_Another_Calculus_Text__A_Short_Introduction_with_Infinitesimals_(Sloughter)/01%3A_Derivatives/1.10%3A_OptimizationOptimization problems, that is, problems in which we seek to find the greatest or smallest value of some quantity, are common in the applications of mathematics. Because of the extreme-value property,...Optimization problems, that is, problems in which we seek to find the greatest or smallest value of some quantity, are common in the applications of mathematics. Because of the extreme-value property, there is a straightforward algorithm for solving optimization problems involving continuous functions on closed and bounded intervals. Hence we will treat this case first before considering functions on other intervals.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/05%3A_Quadratic_Functions/5.06%3A_OptimizationOptimization can be applied to a broad family of different functions. However, in this section, we will concentrate on finding the maximums and minimums of quadratic functions. There is a large body o...Optimization can be applied to a broad family of different functions. However, in this section, we will concentrate on finding the maximums and minimums of quadratic functions. There is a large body of real-life applications that can be modeled by quadratic functions, so we will find that this is an excellent entry point into the study of optimization.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/04%3A_Applications_of_the_Derivative/4.03%3A_OptimizationIn this section we apply the concepts of extreme values to solve "word problems," i.e., problems stated in terms of situations that require us to create the appropriate mathematical framework in which...In this section we apply the concepts of extreme values to solve "word problems," i.e., problems stated in terms of situations that require us to create the appropriate mathematical framework in which to solve the problem.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_VariablesWhen dealing with a function of more than one independent variable, several questions naturally arise. For example, how do we calculate limits of functions of more than one variable? The definition of...When dealing with a function of more than one independent variable, several questions naturally arise. For example, how do we calculate limits of functions of more than one variable? The definition of derivative we used before involved a limit. Does the new definition of derivative involve limits as well? Do the rules of differentiation apply in this context? Can we find relative extrema of functions using derivatives? All these questions are answered in this chapter.
- https://math.libretexts.org/Courses/De_Anza_College/Math_1D%3A_De_Anza/01%3A_Differentiation_of_Functions_of_Several_Variables/1.02%3A_Limits_and_ContinuityWe have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a function of more than one variable, and what it means for a func...We have now examined functions of more than one variable and seen how to graph them. In this section, we see how to take the limit of a function of more than one variable, and what it means for a function of more than one variable to be continuous at a point in its domain. It turns out these concepts have aspects that just don’t occur with functions of one variable.
- https://math.libretexts.org/Learning_Objects/GeoGebra_Simulations/Optimization%3A_Rectangle_Inscribed_in_Parabola_(GeoGebra)
- https://math.libretexts.org/Learning_Objects/GeoGebra_Simulations/Optimization%3A_Getting_Power_to_Island_(GeoGebra)
- https://math.libretexts.org/Bookshelves/Calculus/Elementary_Calculus_2e_(Corral)/04%3A_Applications_of_Derivatives/4.01%3A_OptimizationLet L be the horizontal distance between A and B, let d1 be the distance the light travels from A to the point of contact C with the surface a horizontal distance x from \...Let L be the horizontal distance between A and B, let d1 be the distance the light travels from A to the point of contact C with the surface a horizontal distance x from A, let d2 be the distance from C to B, and let y1 and y2 be the vertical distances from A and B, respectively, to the surface, as in the picture below.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.08%3A_Applied_Optimization_ProblemsOne common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it i...One common application of calculus is calculating the minimum or maximum value of a function. For example, companies often want to minimize production costs or maximize revenue. In manufacturing, it is often desirable to minimize the amount of material used to package a product with a certain volume. In this section, we show how to set up these types of minimization and maximization problems and solve them by using the tools developed in this chapter.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.10%3A_Quadratic_FormsIn this section we use the techniques learned in this chapter to investigate quadratic forms.
