Question: 1. Solve the problem of nding the largest rectangle that can be inscribed in a circle of radius 4 in the following two ways: (a)

1. Solve the problem of nding the largest rectangle that can

1. Solve the problem of nding the largest rectangle that can be inscribed in a circle of radius 4 in the following two ways: (a) Use Calculus I methods. In other words, write down an equation that you want to maxi- mize in terms of :r and y, and use the fact that (12:, y) satises 3:2 +y2 = 1 to get a function of a single variable over a closed interval. Use the extreme value theorem to determine the maximum value of the function

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2. Find out if there are other reference points that can be used as reasonable alternatives.

1. Identify your reference point when making a decision based on an element of risk.

3. If there are reasonable alternatives, think about your decisions based on the different reference points and see if there are any contradictions in the decisions.