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Solve: The Maximum and Minimum Prices of Stock

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Suppose that a company decides to raise capital by selling stock. Over the next 30 years the average monthly price of the stock fluctuates according to the rule S(t)=0.25t^1.20-0.90t+65.85 where S(t) is in dollars per share and t is the number of months since the stock was first offered for sale (this means that S(t) is only valid on the interval [0, 360]). Determine the maximum and minimum prices of the stock and when these prices occurred.

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In about 50 words, a complete solution is given regarding how to determine the prices of stock. All calculations are provided in a step-wise fashion.

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Since S(t)=0.25t^1.20-0.90t+65.85, we take the derivative of S(t) to get ...

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