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Problem 63 Hard Difficulty

If $a$ and $b$ are positive numbers, find the maximum value of $ f(x) = x^a (1 - x)^b $, $ 0 \leqslant x \leqslant 1 $.

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Wen Zheng

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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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Lectures

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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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Problem 16
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Problem 24
Problem 25
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Problem 41
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Problem 43
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Problem 45
Problem 46
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Problem 48
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Problem 50
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Problem 52
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Problem 54
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Problem 80

Video Transcript

using the product Jewel and powerful. We know we can take the derivative we end up with X zero arcs is Juan and axes a over a plus B. These are the places where the driven of zero no, you know that awful 00 off of one is zero and us of a over a plus B was eight of the eighth B to the B over a plus B. The power of a post be the absolute maximum is a over a plus. B is off of a over a plus B, which is eight of the a times B the beat over a plus B the power of a plus b So this is the absolute max.

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Related Topics

Derivatives

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Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor University

Michael Jacobsen

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Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35
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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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