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Problem

If $f$ has a local minimum value at $c$, show tha…

00:44

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Problem 77 Hard Difficulty

Prove that the function
$$ f(x) = x^101 + x^51 + x + 1 $$
has neither a local maximum nor a local minimum.


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00:59

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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Top Calculus 2 / BC Educators
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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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Watch More Solved Questions in Chapter 4

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Problem 9
Problem 10
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Problem 13
Problem 14
Problem 15
Problem 16
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Problem 36
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Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80

Video Transcript

Let's first take the derivative. As we can see, we have positive coefficients and we have powers that are even 150 or both even. Therefore, we know it's always increasing something that's always increasing. Let's say it looks like this or looks like this. It doesn't have a minimum of Maxim because it's always constantly increasing.

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Related Topics

Derivatives

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Video Thumbnail

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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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