- #1
fastblue
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Homework Statement
Show the problem f(x)=((x-a)^2)*((x-b)^2) + x take on a value of a+b/2
for some x?
Can You Solve for a+b/2 in the Continuity Problem f(x)=((x-a)^2)*((x-b)^2) + x?
- Thread starter fastblue
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Homework Help Overview
The problem involves the function f(x)=((x-a)^2)*((x-b)^2) + x and seeks to demonstrate that it can take on the value of (a+b)/2 for some x. The context is rooted in continuity and potentially the application of relevant theorems.
Discussion Character
- Exploratory, Assumption checking, Conceptual clarification
Approaches and Questions Raised
- Participants are attempting to evaluate f(a) and f(b) to understand their implications. Questions about theorems related to continuity and the relationship between f(a), f(b), and (a+b)/2 are being raised.
Discussion Status
There is an ongoing exploration of the function's values at specific points, with some participants expressing confusion about the relationship to (a+b)/2. Hints about the intermediate value theorem have been introduced, suggesting a potential direction for the discussion.
Contextual Notes
Participants are grappling with the definitions and implications of the function's values at a and b, as well as the continuity of the function. There is a noted lack of clarity regarding how these relate to the desired outcome of (a+b)/2.
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