A well-drilling company finds that its marginal profit, in dollars, from drilling a well that is $x$ feet deep is given by $P^{'} (x) = \sqrt[3]{x}$ . Find the company's profit from drilling a well that is 240 feet deep. Round to the nearest cent as needed.
A: $$ 1, 491.47$
B. $$ 1, 118.60$
C. $$ 2, 478.71$
D. $$ 1, 988.63$

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Final Answer: $$ 1, 118.60$

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Step 1 ：The marginal profit is the derivative of the profit function. To find the total profit, we need to integrate the marginal profit function from 0 to 240 feet.

Step 2 ：Let's denote the marginal profit function as $P^{'} (x) = x^{\frac{1}{3}}$ .

Step 3 ：The total profit is then given by the integral of the marginal profit function from 0 to 240, which is $P (x) = \int_{0}^{240} P^{'} (x) d x$ .

Step 4 ：By calculating the integral, we find that the total profit is approximately 1118.60.

Step 5 ：Thus, the company's profit from drilling a well that is 240 feet deep is approximately $1118.60.

Step 6 ：Final Answer: $$ 1, 118.60$

A well-drilling company finds that its marginal profit, in dollars, from drilling a well that is x feet deep is given by P′(x)=x3. Find the company's profit from drilling a well that is 240 feet deep. Round to the nearest cent as needed.A: $1,491.47B. $1,118.60C. $2,478.71D. $1,988.63

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