Finding increasing and decreasing intervals on a graph
Given the function
in
[link] , identify the intervals on which the function appears to be increasing.
We see that the function is not constant on any interval. The function is increasing where it slants upward as we move to the right and decreasing where it slants downward as we move to the right. The function appears to be increasing from
to
and from
on.
In
interval notation , we would say the function appears to be increasing on the interval (1,3) and the interval
Graph the function
Then use the graph to estimate the local extrema of the function and to determine the intervals on which the function is increasing.
Using technology, we find that the graph of the function looks like that in
[link] . It appears there is a low point, or local minimum, between
and
and a mirror-image high point, or local maximum, somewhere between
and
Graph the function
to estimate the local extrema of the function. Use these to determine the intervals on which the function is increasing and decreasing.
The local maximum appears to occur at
and the local minimum occurs at
The function is increasing on
and decreasing on
For the function
whose graph is shown in
[link] , find all local maxima and minima.
Observe the graph of
The graph attains a local maximum at
because it is the highest point in an open interval around
The local maximum is the
-coordinate at
which is
The graph attains a local minimum at
because it is the lowest point in an open interval around
The local minimum is the
y -coordinate at
which is
Analyzing the toolkit functions for increasing or decreasing intervals
We will now return to our toolkit functions and discuss their graphical behavior in
[link] ,
[link] , and
[link] .
Use a graph to locate the absolute maximum and absolute minimum
There is a difference between locating the highest and lowest points on a graph in a region around an open interval (locally) and locating the highest and lowest points on the graph for the entire domain. The
coordinates (output) at the highest and lowest points are called the
absolute maximum and
absolute minimum , respectively.
To locate absolute maxima and minima from a graph, we need to observe the graph to determine where the graph attains it highest and lowest points on the domain of the function. See
[link] .
Not every function has an absolute maximum or minimum value. The toolkit function
is one such function.
Absolute maxima and minima
The
absolute maximum of
at
is
where
for all
in the domain of
The
absolute minimum of
at
is
where
for all
in the domain of
Finding absolute maxima and minima from a graph
For the function
shown in
[link] , find all absolute maxima and minima.
Observe the graph of
The graph attains an absolute maximum in two locations,
and
because at these locations, the graph attains its highest point on the domain of the function. The absolute maximum is the
y -coordinate at
and
which is
The graph attains an absolute minimum at
because it is the lowest point on the domain of the function’s graph. The absolute minimum is the
y -coordinate at
which is
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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