The function f shown in the figure above is continuous on the closed interval (0, 12] and differentiable on the open interval (0, 12). Based on the graph, what are all values of x that satisfy the conclusion of the Mean Value Theorem applied to f on the closed interval [0, 12] ? A 4.5 only because this is the value where f (x) equals the average rate of change of f on [0, 12]. B 3 and 8 because these are the values where f' (x) = 0 on [0, 12]. 2 and 9 only because these are the values where the instantaneous rate of change of fat those values is equal to the average rate of change of f on [0, 12]. 2, 4.5, and 9 because these are the values where either the instantaneous rate of change of fat the value is equal to the average rate of change of f on (0, 12 or the value of D f (x) is equal to the average rate of change of f on [0, 12].

Question
The function f shown in the figure above is continuous on the closed interval (0, 12] and differentiable on the open interval (0, 12). Based on the graph, what are all values of x that satisfy the
conclusion of the Mean Value Theorem applied to f on the closed interval [0, 12] ?
A
4.5 only because this is the value where f (x) equals the average rate of change of f on [0, 12].
B
3 and 8 because these are the values where f' (x) = 0 on [0, 12].
2 and 9 only because these are the values where the instantaneous rate of change of fat those values is equal to the average rate of change of f on [0, 12].
2, 4.5, and 9 because these are the values where either the instantaneous rate of change of fat the value is equal to the average rate of change of f on (0, 12 or the value of
D
f (x) is equal to the average rate of change of f on [0, 12].
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Transcribed Image Text

The function f shown in the figure above is continuous on the closed interval (0, 12] and differentiable on the open interval (0, 12). Based on the graph, what are all values of x that satisfy the conclusion of the Mean Value Theorem applied to f on the closed interval [0, 12] ? A 4.5 only because this is the value where f (x) equals the average rate of change of f on [0, 12]. B 3 and 8 because these are the values where f' (x) = 0 on [0, 12]. 2 and 9 only because these are the values where the instantaneous rate of change of fat those values is equal to the average rate of change of f on [0, 12]. 2, 4.5, and 9 because these are the values where either the instantaneous rate of change of fat the value is equal to the average rate of change of f on (0, 12 or the value of D f (x) is equal to the average rate of change of f on [0, 12].

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