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Let f(x) be the function shown in the graph below. Click on the graph to enlarge it.

a. State the point at which f has an absolute minimum
b State the point at which f has an absolute maximum
c.Complete each of the following statements: (i) The function attains a local at x=2. (ii) The function attains a local at x=4. (iii) The function attains a local at x=5. Suppose f(x) =xe⁻⁷ˣ,0≤x≤2.Use the Closed Interval Method to find points at which the absolute extrema of f occur.

User Rui
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1 Answer

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Final answer:

The question addresses the evaluation of a function's minimums and maximums and the application of the Closed Interval Method, but without the provided graph or explicit function details, the exact points for absolute extrema cannot be determined.

Step-by-step explanation:

The student has presented several components within a question related to the analysis of a function's graph and the use of the Closed Interval Method to find extrema. However, the graph mentioned in the question is not provided, which limits the ability to give specific points for the absolute minimum and maximum. Without loss of generality, for a function graphed between 0 ≤ x ≤ 20, we can state that the absolute minimum and maximum would be found either at the endpoints of the interval or at critical points where the derivative of the function equals zero within the interval.

Local minimums and maximums are found by analyzing the function's first and second derivatives, but without the actual function or its graph, we cannot specify where these local extrema occur.

The Closed Interval Method involves evaluating the function at its critical points within the interval and at the endpoints to determine the absolute extrema. Unfortunately, without access to the graph or specific function, we cannot apply this method precisely to ascertain absolute minimum and maximum values.

User Mark Canlas
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