2 nd Saturday Sections 2.2 – 2.5. The graph shows the profit (in $thousands) from the sale of x hundred widgets. Use a tangent line to estimate and interpret.

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Presentation transcript:

2 nd Saturday Sections 2.2 – 2.5

The graph shows the profit (in $thousands) from the sale of x hundred widgets. Use a tangent line to estimate and interpret the instantaneous rate of change at x = 2.5. Example 1

The graph shows the profit (in $thousands) from the sale of x hundred widgets. Use a tangent line to estimate and interpret the instantaneous rate of change at x = 2.5. Example 1 cont.

The graph shows the distance a moving particle has moved (in meters) after x seconds. Find the particle’s speed at the 5 second mark. Example 2

The graph shows the distance a moving particle has moved (in meters) after x seconds. Find the particle’s speed at the 5 second mark. Example 2 cont.

A certain town had a population of in 2010 and was growing at a rate of 1500 people per year. What was the percent rate of change in the population of this town in that year? Example 3

The graph shows the amount (in grams) of a certain radioactive substance that remains x hours after an experiment began. Estimate the percent rate of change after 5 hours. Example 4

The graph shows the amount (in grams) of a certain radioactive substance that remains x hours after an experiment began. Estimate the percent rate of change after 5 hours. Example 4 cont.

Suppose P(n) gives the profit in $thousand when n hundred widgets are sold. Interpret the following. (a) and (b) and Example 5

Suppose T(p) gives the number of airline tickets sold from Washington D.C. to Boston that are sold when the price is $p. Interpret the following. (a) (b) (c) when p = 180 Example 6

Use the graph below to estimate and. Example 7

Use the graph below to estimate and. Example 7 cont.

Consider the function. Numerically estimate the value of. Example 8

The temperature x hours after midnight during a typical day in May in a Midwestern city can be modeled by: °F Numerically estimate the rate at which the temperature is changing at 10:30 AM. Example 9

The table gives the number of students per computer in US public schools in various years. Find the most appropriate model and use it to numerically estimate and interpret the rate of change in this quantity in Example 10 Year Students

Consider the function. Numerically estimate the value of. Example 11

Suppose the profit (in $) from the sale of x blenders can be modeled by the function. Algebraically find and interpret. Example 12

Suppose the profit (in $) from the sale of x blenders can be modeled by the function. Algebraically find a formula for. Use this to find and interpret. Example 13

The temperature x hours after midnight during a typical day in May in a Midwestern city can be modeled by: °F (a)Find a formula for the rate of change in temperature on a typical May day in this town (b)Calculate the percentage rate of change in temperature at 11:15 AM. Example 14

The table gives the average age of women at the time of their first marriage in various years. (a)Let x be the years since 1960, then algebraically construct a model for the rate of change in the average age of women at the time of their first marriage. (b)Find and interpret. Example 15 Year Age