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
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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