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A company that manufactures a certain type of gardening tool determines its profit is dependent upon the sales price of the tool. The yearly profit can be modeled by the function

P(x)=−5.1(x−21.75)2+62.80

where P(x) represents the profit in thousands of dollars and x is the sales price (in dollars) of the tool.
Which of the following statements is true?
The minimum profit of $21.75 thousand occurs when the sales price of the tool is $62.80.
The minimum profit of $62.80 thousand occurs when the sales price of the tool is $21.75.
The maximum profit of $21.75 thousand occurs when the sales price of the tool is $62.80.
The maximum profit of $62.80 thousand occurs when the sales price of the tool is $21.75.

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