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Prove Fermat's Theorem for the case in which $f$ …

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Problem 78 Hard Difficulty

If $f$ has a local minimum value at $c$, show that the function $ g(x) = - f(x) $ has a local maximum value at $c$.


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WZ

Wen Zheng

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Related Topics

Derivatives

Differentiation

Volume

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04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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06:14

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Video Transcript

okay, We know that the derivative of negative FX is negative to the original parent function, which is FX. Therefore, we know the local maximum is a point in this context, and we know it's the point where the function changes from increasing to decreasing and the local minima, by contrast, is where function changes from decreasing to increasing. We know the function is decreasing before X equal, see and increasing just after x equal. See, we know that increasing and decreasing behaviors opposite. Therefore, we note there Haas to be a local maximum at X equal, see

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Related Topics

Derivatives

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Kayleah Tsai

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Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Join Course
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