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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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02:33
Wen Zheng
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 1
Maximum and Minimum Values
Derivatives
Differentiation
Volume
Missouri State University
Oregon State University
Baylor University
Idaho State University
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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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