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# MAT 142 Calculus For Business For Marginal And Average Cost Function

## Questions:

A company lists its profit function as

P(x) = 8x – 0.02x2 – 500

Where x is the number of napkins made (in millions) and P is the profit in hundreds of dollars.

a. Graph the function.

b. Find the instantaneous rate of change in profit at x = 100.
(You should not use the definition of the derivative.)

c. Find the instantaneous rate of change in profit at x = 200.
(You should not use the definition of the derivative.)

d. Find the profit at x = 200.

e. Write a sentence interpreting question b. Use the correct units.

f. Interpret parts b, c, and d on the graph of part a.

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