A homeowner sets the thermostat so that the temperature in the house begins to drop from
at
p.m., reaches a low of
during the night, and rises back to
by
a.m. the next morning. Suppose that the temperature in the house is given by
for
where
is the number of hours past
p.m. Find the instantaneous rate of change of the temperature at midnight.
Since midnight is
hours past
p.m., we want to compute
Refer to
[link] .
The instantaneous rate of change of the temperature at midnight is
per hour.
A toy company can sell
electronic gaming systems at a price of
dollars per gaming system. The cost of manufacturing
systems is given by
dollars. Find the rate of change of profit when
games are produced. Should the toy company increase or decrease production?
The profit
earned by producing
gaming systems is
where
is the revenue obtained from the sale of
games. Since the company can sell
games at
per game,
Consequently,
Therefore, evaluating the rate of change of profit gives
Since the rate of change of profit
and
the company should increase production.
A coffee shop determines that the daily profit on scones obtained by charging
dollars per scone is
The coffee shop currently charges
per scone. Find
the rate of change of profit when the price is
and decide whether or not the coffee shop should consider raising or lowering its prices on scones.
The slope of the tangent line to a curve measures the instantaneous rate of change of a curve. We can calculate it by finding the limit of the difference quotient or the difference quotient with increment
The derivative of a function
at a value
is found using either of the definitions for the slope of the tangent line.
Velocity is the rate of change of position. As such, the velocity
at time
is the derivative of the position
at time
Average velocity is given by
Instantaneous velocity is given by
We may estimate a derivative by using a table of values.
Key equations
Difference quotient
Difference quotient with increment
Slope of tangent line
Derivative ofat
Average velocity
Instantaneous velocity
For the following exercises, use
[link] to find the slope of the secant line between the values
and
for each function
Questions & Answers
Examine the distinction between theory of comparative cost Advantage and theory of factor proportion
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
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