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1. Extrema (Local and Absolute) | Brilliant Math & Science Wiki
Link: https://brilliant.org/wiki/extrema/
Description: WebExtrema (maximum and minimum values) are important because they provide a lot of information about a function and aid in answering questions of optimality. Calculus provides a variety of tools to help quickly determine the location and nature of extrema. Contents. Global Extrema. Local Extrema. Differentiable Functions. See Also. Global Extrema.
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2. Worked example: absolute and relative extrema - Khan Academy
Link: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:maximum-and-minimum-points/v/identifying-relative-and-absolute-maxima-and-minima
Description: WebExtrema is the general name for maximum and minimum points. This video shows how to identify relative and absolute extrema in the graph of a function.
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3. Extrema of a Function - Simon Fraser University
Link: https://www.sfu.ca/math-coursenotes/Math%20157%20Course%20Notes/sec_Extrema.html
Description: Web5.5.1 Relative Extrema. ¶. A relative maximum point on a function is a point (x, y) on the graph of the function whose y -coordinate is larger than all other y -coordinates on the graph at points “close to” (x, y). More precisely, (x, f(x)) is a relative maximum if there is an interval (a, b) with a < x < b and f(x) ≥ f(z) for every z in ...
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4. 4.1: Extreme Values of Functions - Mathematics LibreTexts
Link: https://math.libretexts.org/Courses/University_of_California_Davis/UCD_Mat_21A%3A_Differential_Calculus/4%3A_Applications_of_Definite_Integrals/4.1%3A_Extreme_Values_of_Functions
Description: WebLocating Absolute Extrema. The extreme value theorem states that a continuous function over a closed, bounded interval has an absolute maximum and an absolute minimum. As shown in Figure \(\PageIndex{2}\), one or both of these absolute extrema could occur at …
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5. Calculus I - Finding Absolute Extrema - Pauls Online Math Notes
Link: https://tutorial.math.lamar.edu/Classes/CalcI/AbsExtrema.aspx
Description: WebNov 16, 2022 · Example 1 Determine the absolute extrema for the following function and interval. g(t) = 2t3 +3t2 −12t+4 on [−4,2] g ( t) = 2 t 3 + 3 t 2 − 12 t + 4 on [ − 4, 2] Show Solution. In this example we saw that absolute extrema can and will occur at both endpoints and critical points.
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6. 6.3: Extrema and Models - Mathematics LibreTexts
Link: https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/06%3A_Polynomial_Functions/6.03%3A_Extrema_and_Models
Description: WebExtrema. Before we begin, we’d first like to differentiate between local extrema and absolute extrema. This is best accomplished by means of an example. Consider, if you will, the graphs of three polynomial functions in Figure 1. In the first figure, Figure \(\PageIndex{1a}\), the point A is the “absolute” lowest point on the graph.
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7. LECTURE 12: EXTREMA. - Mathematics
Link: https://math.jhu.edu/~brown/courses/s19/Lectures/Lecture12.pdf
Description: WebLECTURE 12: EXTREMA. 110.211 HONORS MULTIVARIABLE CALCULUS PROFESSOR RICHARD BROWN. Synopsis. Local and global extrema are much like their counterparts in single variable calculus. They are just points in the domain of a real-valued function where the function value is locally the lowest or highest.
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8. Extrema - Emory University
Link: https://mathcenter.oxford.emory.edu/site/math111/extrema/
Description: WebThe Extreme Value Theorem. If f f is continuous on [a, b] [ a, b], then f f has an absolute maximum and an absolute minimum in [a, b] [ a, b]. Fermat's Theorem. If f f is differentiable at c c and f(c) f ( c) is a local extremum, then f′(c) = 0 f ′ ( c) = 0. Consider carefully how these can be used in conjunction with one another to find ...
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9. Extrema and Critical Points | Calculus I - Lumen Learning
Link: https://courses.lumenlearning.com/calculus1/chapter/extrema-and-critical-points/
Description: WebExplain how to find the critical points of a function over a closed interval. Describe how to use critical points to locate absolute extrema over a closed interval. Absolute Extrema. Consider the function f (x) =x2 +1 f ( x) = x 2 + 1 over the interval (−∞,∞) ( − ∞, ∞). As x→ ±∞ x → ± ∞, f (x)→ ∞ f ( x) → ∞.
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10. Extrema | Definition & Meaning - The Story of Mathematics
Link: https://www.storyofmathematics.com/glossary/extrema/
Description: WebExtrema|Definition & Meaning. Definition. A function’s extremum, or (highest value), is the point at which the function’s maximum or minimum value is obtained over a given range.