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A number $ a $ is called a fixed point of a function $ f $ if $ f(a) = a $. Prove that if $ f'(x) \not= 1 $ for all real numbers $ x $, then $ f $ has at most one fixed point.

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Fixed point couldn't exist more than 1

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 2

The Mean Value Theorem

Derivatives

Differentiation

Volume

Missouri State University

Baylor University

Boston College

Lectures

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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.

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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.

01:24

A number a is called a fix…

01:57

A number $a$ is called a f…

01:59

A number $c$ is called a f…

01:31

A fixed point of a functio…

01:51

so we're showing that F of X is equal to acts. That's only one solution is, uh, derivative of X is not equal to one. We have the function G of acts. We're gonna make it equal to F X minus. That's then we have the derivative of G of X is equal to the derivative of EPA VAX minus one is not equal to zero. Then we're gonna apply rules. Zero. You see that G FX has only 10 so f of X equals acts passed only one solution.

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