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## PowerPoint Slideshow about ' section 4.1' - halla-hobbs

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1. Find the indefinite integral.

b. Graph the five functions 1/3 x 3 – 2, 1/3 x 3 – 1,

1/3 x 3 , 1/3 x 3 + 1, 1/3 x 3 + 2, on the window [-3, 3] and [-5, 5].

c. Find the derivatives at x = 2 of the five functions in part b.

c. For x = 2, the slope of each curve is 4. Thus, the derivative of each curve is x2 .

- BUSINESS: Cost – A company’s marginal cost function is
- MC = 20 x 3/2 – 15 x 2/3 + 1, where x is the number of units, and fixed cost are $4000. Find the cost function.

13. BUSINESS: Revenue – A company’s marginal revenue function is

MR = 12 x 1/3 + 3 x ½ , where x is the number of units. Find the revenue function.

- GENERAL : Learning – A person can memorize words at a rate of 3/t words per minute.
- Find a formula for the total number of words that can be memorized in t minutes.
- Use that formula to find the total number of words that can be memorized in 25 minutes.

b. After 25 minutes, the total number of words

memorized is N(25) = 6(25) 1/2 = 30 words

- ENVIRONMENTAL SCIENCE: Pollution – A chemical plant is adding pollution to a lake at the rate of 40t 3 tons per year, where t is the number of years that the plant has been in operation.
- a. Find a formula for the total amount of pollution that will enter the lake in the first t years of the plant’s operation.
- b. Use the formula that you just found to find out how much pollution will enter the lake in the first 4 years of the plant’s operation.
- c. If all life in the lake will cease when 400 tons of pollution have entered the lake, will the lake live beyond 4 years?

b. P(4) = 16(4) 5/ 2 = 512 tons

Thus, 512 tons of pollution will enter the

lake in the first four years of the plant’s

operation.

c. No, since 512 > 400.

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