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Use the mean value theorem and find all points 0 < c < 2 such that f(2) − f(0) = f '(c)(2 − 0). (enter your answers as a comma-separated list.)

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Final answer:

The Mean Value Theorem cannot be directly applied without knowing the function f(x). The theorem indicates that for a continuous and differentiable function, a point c exists that equates the derivative to the average rate of change over a given interval.

Step-by-step explanation:

To use the Mean Value Theorem to find all points c such that 0 < c < 2 and f(2) − f(0) = f'(c)(2 − 0), we need to know the function f(x). However, since the function is not provided, it is not possible to apply the theorem directly. Generally, the Mean Value Theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) so that f'(c) = (f(b) - f(a)) / (b - a). To find the points c for a specific function, we would take the derivative of the function, set it equal to the average rate of change over the interval, and solve for c.

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