Final answer:
The question about finding a value of c for the function f(x) is incomplete and cannot be answered without additional information. Without a complete question, we cannot properly apply the Intermediate Value Theorem, Mean Value Theorem, or Extreme Value Theorem to find or disprove the existence of c.
Step-by-step explanation:
The subject of the question revolves around verifying the possibility of a certain value c existing for the function f(x) = 2 - |2x-1| using different mathematical theorems. However, the question seems to be incomplete or incorrectly stated, as there is a missing condition or equation after f(3). Therefore, without additional information, it is impossible to directly apply the given mathematical theorems to prove or disprove the existence of c.
To apply these theorems:
A) To use contradiction, we need a statement involving c that we assume to be true and then show that it leads to a contradiction.
B) The Intermediate Value Theorem requires that f(x) is continuous on a closed interval and takes on every value between f(a) and f(b).
C) The Mean Value Theorem applies if f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).
D) The Extreme Value Theorem applies if f(x) is continuous over a closed interval [a, b], ensuring the function attains a maximum and minimum value on that interval.
Without the completion of the prompt or additional context, none of these methods can be properly utilized to address the question about the existence of the value c. In a standard scenario, to calculate the change (strong>A), one would substitute the x and t values of the chosen points into an equation and use the final value minus the initial value.
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