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- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/MAT-204%3A_Differential_Equations_for_Science_(Lebl_and_Trench)/10%3A_Nonlinear_Systems/10.02%3A_Stability_and_Classication_of_Isolated_Critical_PointsA critical point is isolated if it is the only critical point in some small "neighborhood" of the point. That is, if we zoom in far enough it is the only critical point we see. In the above example, t...A critical point is isolated if it is the only critical point in some small "neighborhood" of the point. That is, if we zoom in far enough it is the only critical point we see. In the above example, the critical point was isolated. If on the other hand there would be a whole curve of critical points, then it would not be isolated.
- https://math.libretexts.org/Courses/Butler_Community_College/MA148%3A_Calculus_with_Applications_-_Butler_CC/04%3A_Functions_of_Two_Variables/4.03%3A_OptimizationThe partial derivatives tell us something about where a surface has local maxima and minima. Remember that even in the one-variable cases, there were critical points which were neither maxima nor mini...The partial derivatives tell us something about where a surface has local maxima and minima. Remember that even in the one-variable cases, there were critical points which were neither maxima nor minima – this is also true for functions of many variables. In fact, as you might expect, the situation is even more complicated.
- https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/04%3A_Applications_of_Derivatives/4.02%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
- https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/04%3A_Applications_of_Derivatives/4.01%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q1/04%3A_Applications_of_Derivatives/4.04%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Tran)/04%3A_Applications_of_Derivatives/4.03%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
- https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Everett)/04%3A_Applications_of_Derivatives/4.03%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
- https://math.libretexts.org/Courses/Prince_Georges_Community_College/MAT_2410%3A_Calculus_1_(Beck)/04%3A_Applications_of_Derivatives/4.04%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/Chapter_4%3A_Applications_of_Derivatives/4.2%3A_Maxima_and_MinimaFrom the graph of \(f\) in Figure, we see that f has an absolute maximum at \(x=1\) and an absolute minimum at \(x=−1.\) Hence, \(f\) has a local maximum at \(x=1\) and a local minimum at \(x=−1\). (N...From the graph of \(f\) in Figure, we see that f has an absolute maximum at \(x=1\) and an absolute minimum at \(x=−1.\) Hence, \(f\) has a local maximum at \(x=1\) and a local minimum at \(x=−1\). (Note that if \(f\) has an absolute extremum over an interval \(I\) at a point \(c\) that is not an endpoint of \(I\), then \(f\) has a local extremum at \(c.)\)
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/04%3A_Appropriate_Applications/4.01%3A_Graphing_Using_Calculus_-_Maxima_and_MinimaThis section covers how to use calculus to graph functions by finding critical points, maxima, and minima. It explains how the first and second derivative tests help identify increasing or decreasing ...This section covers how to use calculus to graph functions by finding critical points, maxima, and minima. It explains how the first and second derivative tests help identify increasing or decreasing intervals and concavity, which are key to determining the shape of the graph. The section also demonstrates how to apply these concepts to real-world problems, optimizing functions to find their maximum or minimum values.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/04%3A_Applications_of_Derivatives/4.03%3A_Maxima_and_MinimaFinding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of mate...Finding the maximum and minimum values of a function has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach. In this section, we look at how to use derivatives to find the largest and smallest values for a function.
