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- Derivatives
- Derivatives as rates of change
Suppose that the profit obtained from the sale of
fish-fry dinners is given by
Use the marginal profit function to estimate the profit from the sale of the 101st fish-fry dinner.
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Key concepts
- Using
it is possible to estimate
given
and
- The rate of change of position is velocity, and the rate of change of velocity is acceleration. Speed is the absolute value, or magnitude, of velocity.
- The population growth rate and the present population can be used to predict the size of a future population.
- Marginal cost, marginal revenue, and marginal profit functions can be used to predict, respectively, the cost of producing one more item, the revenue obtained by selling one more item, and the profit obtained by producing and selling one more item.
For the following exercises, the given functions represent the position of a particle traveling along a horizontal line.
- Find the velocity and acceleration functions.
- Determine the time intervals when the object is slowing down or speeding up.
a.
b. speeds up
slows down
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A rocket is fired vertically upward from the ground. The distance
in feet that the rocket travels from the ground after
seconds is given by
- Find the velocity of the rocket 3 seconds after being fired.
- Find the acceleration of the rocket 3 seconds after being fired.
a.
b.
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A ball is thrown downward with a speed of 8 ft/s from the top of a 64-foot-tall building. After
t seconds, its height above the ground is given by
- Determine how long it takes for the ball to hit the ground.
- Determine the velocity of the ball when it hits the ground.
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The position function
represents the position of the back of a car backing out of a driveway and then driving in a straight line, where
is in feet and
is in seconds. In this case,
represents the time at which the back of the car is at the garage door, so
is the starting position of the car, 4 feet inside the garage.
- Determine the velocity of the car when
- Determine the velocity of the car when
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The position of a hummingbird flying along a straight line in
seconds is given by
meters.
- Determine the velocity of the bird at
sec.
- Determine the acceleration of the bird at
sec.
- Determine the acceleration of the bird when the velocity equals 0.
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A potato is launched vertically upward with an initial velocity of 100 ft/s from a potato gun at the top of an 85-foot-tall building. The distance in feet that the potato travels from the ground after
seconds is given by
- Find the velocity of the potato after
and
- Find the speed of the potato at 0.5 s and 5.75 s.
- Determine when the potato reaches its maximum height.
- Find the acceleration of the potato at 0.5 s and 1.5 s.
- Determine how long the potato is in the air.
- Determine the velocity of the potato upon hitting the ground.
a. 84 ft/s, −84 ft/s b. 84 ft/s c.
d.
in both cases e.
f.
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Questions & Answers
how does Neisseria cause meningitis
is the branch of biology that deals with the study of microorganisms.
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
How bacteria create energy to survive?
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
which site have a normal flora
Many sites of the body have it
Skin
Nasal cavity
Oral cavity
Gastro intestinal tract
Safaa
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Binomial nomenclature
adeolu
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Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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