Solve 5 Problems: Get Help Now!

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Homework Help Overview

The discussion revolves around applying the Mean Value Theorem to a specific function, f(x) = (16 - x^2)^(1/2), over the interval [-4, 4]. Participants are exploring whether the conditions of the theorem are satisfied and are seeking assistance in determining the appropriate value of C.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to verify if the function meets the criteria for the Mean Value Theorem and is questioning their differentiation process. Other participants are providing feedback on the differentiation and guiding the poster towards finding the necessary point C.

Discussion Status

The discussion is active, with participants providing feedback on the differentiation and prompting further exploration of the Mean Value Theorem's application. There is a collaborative effort to clarify the conditions needed for the theorem.

Contextual Notes

Participants are reminded of the forum's requirement to show work before receiving help, which may influence the depth of responses. The original poster expresses uncertainty about their understanding of the theorem and differentiation.

Mellivice
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What are you having problems with. You have to show some work for each of the problems before getting any help here.
 
Ok for question 2 i need to see if in part A if it statisfys the Mean Value Theorem, and if it does which is the value of C which statistfies the condition of the theorem

f(x)=(16-x^2)^1/2 on [-4,4]

if differentiate it should like this or i am not smart

-x/(16-x^2)^1/2

From the looks of it it does not but i just want to see anyone elses opinion
 
Your differentiation is OK, now you need to find a point c in (-4,4) which satisfies:

[tex]f'(c)=\frac{f(4)-f(-4)}{4-(-4)}[/tex]
 

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