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- https://math.libretexts.org/Courses/Coastline_College/Math_C280%3A_Calculus_III_(Tran)/03%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/3.09%3A_Optimization_of_Functions_of_Several_VariablesThe application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier...The application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/14%3A_Differentiation_of_Functions_of_Several_Variables/14.08%3A_Maxima_Minima_ProblemsThe application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier...The application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.
- https://math.libretexts.org/Courses/Montana_State_University/M273%3A_Multivariable_Calculus/14%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/Optimization_of_Functions_of_Several_VariablesThe application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier...The application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_v2_(Reed)/14%3A_Differentiation_of_Functions_of_Several_Variables/14.07%3A_Maxima_Minima_ProblemsThe application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier...The application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/04%3A_Parametric_Equations/4.02%3A_Calculus_of_Parametric_CurvesNow that we have introduced the concept of a parameterized curve, our next step is to learn how to work with this concept in the context of calculus. For example, if we know a parameterization of a gi...Now that we have introduced the concept of a parameterized curve, our next step is to learn how to work with this concept in the context of calculus. For example, if we know a parameterization of a given curve, is it possible to calculate the slope of a tangent line to the curve? How about the arc length of the curve? Or the area under the curve?
- 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/Bookshelves/Calculus/Differential_Calculus_for_the_Life_Sciences_(Edelstein-Keshet)/06%3A_Sketching_the_Graph_of_a_Function_using_Calculus_Tools/6.02%3A_Special_Points_on_the_Graph_of_a_FunctionIn this section we use tools of algebra and calculus to identify special points on the graph of a function. We first consider the zeros of a function, and then its critical points.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/14%3A_Differentiation_of_Functions_of_Several_Variables/14.07%3A_Maxima_Minima_ProblemsThe application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier...The application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_I%3A_Differential_Calculus/04%3A_Applications_of_Derivatives/4.04%3A_The_Mean_Value_TheoremThe Mean Value Theorem is one of the most important theorems in calculus. We look at some of its implications at the end of this section. First, let’s start with a special case of the Mean Value Theor...The Mean Value Theorem is one of the most important theorems in calculus. We look at some of its implications at the end of this section. First, let’s start with a special case of the Mean Value Theorem, called Rolle’s theorem.
- 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/Monroe_Community_College/MTH_212_Calculus_III/Chapter_13%3A_Functions_of_Multiple_Variables_and_Partial_Derivatives/13.8%3A_Optimization_of_Functions_of_Several_VariablesThe application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier...The application derivatives of a function of one variable is the determination of maximum and/or minimum values is also important for functions of two or more variables, but as we have seen in earlier sections of this chapter, the introduction of more independent variables leads to more possible outcomes for the calculations. The main ideas of finding critical points and using derivative tests are still valid, but new wrinkles appear when assessing the results.
