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- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/11%3A_Appendix_-_Prerequisite_Function_Material/11.05%3A_Graphing_Functions_by_Point-PlottingIt’s time to look at functions graphically again, only this time we’ll do so with the notation defined in Section 1.4.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/01%3A_Relations_and_Functions/1.06%3A_Graphs_of_FunctionsIt’s time to look at functions graphically again, only this time we’ll do so with the notation defined in Section 1.4.
- https://math.libretexts.org/Courses/Hope_College/Math_126_-_Calculus_with_Review_II/02%3A_Using_Derivatives/2.02%3A_Using_Derivatives_to_Identify_Extreme_ValuesThe critical numbers of a continuous function f are the values of p for which f′(p)=0 or f′(p) does not exist. These values are important because they identify horizontal tangent lines or corner p...The critical numbers of a continuous function f are the values of p for which f′(p)=0 or f′(p) does not exist. These values are important because they identify horizontal tangent lines or corner points on the graph, which are the only possible locations at which a local maximum or local minimum can occur.
- 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.
