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On the closed interval [-0.5,1.2], determine the absolute minimum output value f and the absolute maximum output value f.

A) Absolute minimum at f=−0.5 and absolute maximum at f=1.2.
B) Absolute minimum at f=0 and absolute maximum at f=1.2.
C) Absolute minimum at f=−0.5 and absolute maximum at f=0.
D) Absolute minimum at f=1.2 and absolute maximum at f=−0.5.

User JakeB
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Final answer:

For a horizontal line described by the function f(x) = 20 over an interval [0, 20], the constant value of the function is both the absolute minimum and maximum. To determine these values for a specific function on the closed interval [-0.5, 1.2], one needs the actual function's formula, which was not provided.

Step-by-step explanation:

To find the absolute minimum and maximum output values of a function on a closed interval, we must examine the endpoints of the interval and any critical points within the interval where the derivative is zero or undefined. For the function described as a horizontal line, with an equation f(x) = 20 for 0 ≤ x ≤ 20, there are no critical points since the derivative of a constant function is zero. Therefore, the function maintains the same value across the entire interval. In this case, both the absolute minimum and maximum output values of the function are the constant value of the function, which is 20.

The answer to the student's question specifically would depend on the actual function f(x) they are referring to. As there's no indication that the function changes within the given interval of [-0.5,1.2], we cannot determine the answer based on the information provided. If the function is indeed constant, as in the given reference where f(x) = 20, then the minimum and maximum would be the same at the constant value.

User Ryandesign
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