2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the...

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2.3 RATES OF CHANGE Calc 10/1/14

Transcript of 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the...

Page 1: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

2.3 RATES OF CHANGE

Calc 10/1/14

Page 2: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Warm-up•1. Determine any points at which the graph has horizontal tangents:

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2. A College club raises funds by selling candy bars for $1.00 each. The club pays $0.60 for each candy bar and has annual fixed costs of $250. Write the profit P as a function of x, the number of candy bars sold.

Page 3: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

2.3 Rates of Change - Marginals• What were the rates in the warm-up problem?

Page 4: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Rates of Change in Economics - Marginals

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Page 5: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Discrete vs. Continuous

Page 6: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Finding the marginal profit•The profit derived from selling x units of an iphone charger is given by:

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•Find the marginal profit for a production level of 50 units.

•Compare this with the actual gain in profit obtained by increasing production level from 50 to 51.

Page 7: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Demand and Revenue• Demand function - # of units, x, consumers are willing to purchase at a given price, p

•Total Revenue – related to the price per unit and the quantity demanded(or sold)

𝑝 (𝑥)

Page 8: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Finding a demand function (Ex. 6)

•A business sells 2000 items per month at a price of $10 each. It is estimated that monthly sales will increase 250 units for each $0.25 reduction in price. Use the information to find the demand function and total revenue function.

Page 9: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Marginal Revenue

Page 10: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Finding Marginal revenue• Chick-fil-A has determined that the monthly demand for their spicy chicken sandwich is given by:

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•Find the increase in revenue per chicken sandwich for monthly sales of 20,000 sandwiches. (find marginal revenue when x=20,000)

Page 11: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

Finding Marginal Profit• Suppose the cost in producing chicken sandwiches is

Find the profit and marginal profit for each production level

a) = 20,000 b)30,000

Page 12: 2.3 RATES OF CHANGE Calc 10/1/14. Warm-up 2.3 Rates of Change - Marginals What were the rates in the warm-up problem?

What is the meaning of marginal profit at a given value?


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WARM-UP RATES AND BODY TEMPERATURES IN BEES: THE ... · Warm-up rates and body temperatures in bees 305 Heinrich, 1987). May (1976) and Bartholomew (1981) have suggested that, in

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Contents · Web view58 6.9 18 2.1 Q2 2018 40 4.6 20 2.3 Q3 2018 54* 5.8* 24* 2.6* * rates and numbers include unvalidated date from RHH Table 8 Hospital numbers and rates per10 000

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Warm Up Do you think crime rates in America are low or high? What are you basing your response on?

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Warm Up Determine a) ∞ b) 0 c) ½ d) 3/10 e) 1. 2.4 – Rates of Change and Tangent Lines.

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4-2 Rates Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

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01/18/11 Unit Rates Today’s Plan: -Warm-Up & Test Results -Unit Rates Lesson -Unit Rates Assignment Learning Target: I will calculate and compare unit.

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WARM WARM - ASUWELL

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