-
Home
- Calculus volume 1
- 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.
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
Questions & Answers
the study of living organisms and their interactions with one another and their environments
AI-Robot
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
Google Play and the Google Play logo are trademarks of Google Inc.