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- 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.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Raji)/03%3A_Congruences/3.05%3A_Theorems_of_Fermat_Euler_and_WilsonIn this section we present three applications of congruences. The first theorem is Wilson’s theorem which states that (p−1)!+1 is divisible by p , for p prime. Next, we present Fermat’s theorem, a...In this section we present three applications of congruences. The first theorem is Wilson’s theorem which states that (p−1)!+1 is divisible by p , for p prime. Next, we present Fermat’s theorem, also known as Fermat’s little theorem which states that ap and a have the same remainders when divided by p where p∤a . Finally we present Euler’s theorem which is a generalization of Fermat’s theorem and it states that for any positive integer m that is relatively prime to an integer a.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/04%3A_Applications_of_Derivatives/4.03%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.)
