Local Max & Min Extrema on the TI-89: Raw Transcript
This is a video on a program app for the texas instruments ti 89
titanium calculator that I’ve programmed
with regard to graphing by hand where we’re going to find
the local extrema or the local maximum and minimums
and to get into my menu you have to press second alpha
then the letters i n d e x and then press alpha again
to enter the open and closed parenthesis press enter
and you are into my menu you scroll down
all alphebetical to what you want
there’s many many things in my menu here for calculus
for you to pass calculus do your homework etcetra
right now we want to find local max and mins I tell you to start a graph on your paper
and we’re going to enter our function you have to enter alpha before you enter anything
in these entry lines in my programs alpha, and were going to do this function
three times x squared minus x to the fourth power
i show you what you’ve entered so in case you’ve made a mistake you can change
it give you that option
I say it’s ok We want to find local max and mins
you can find all of these things critical points
crosses x axis crosses y axis
all to get your graphing by hand perfect we want to know what local maximum and mins
you take the first function take the first derivative
you factor that and you get your critical numbers
these are where these points cross the x axis in this graph
mark them on your graph right now x equals one point two two
on the right side of the zero and negative here
ah, we need to find the critical points that’s where you add the y value
so you need to plug these critical numbers into the original function to get the critical
point and here’s the x y value right now one point
two two I show you what to do
you wrirte this stuff down on your paper so you get an a on this problem
exactly as you see it and here’s the x and y value for that critical
point the next one is zero
the critical point is zero zero and for the minus one point two two
the critical point is minus one point two two and two point two five
that’s the x y value so those are the critical points
next thing you want to find you want to do the second derivative test
to find the local maximum or local minimum if they are a minimum, I like to put a valley
on that critical point that you’ve marked on your graph already
and if it’s a maximum I put a mountain right there
a small tiny mountain at that point so it tells me when I draw the graph
as to how to what is going to happen on that anyways to do the second derivative test
you find the second derivative after you find the first one
which I do for you and you plug that critical point into the
second derivative and the anwer is either negative or positive
if it’s negative its a maximum in this case put the zero in there
comes up with six that’s a minimum
and minus twenty two comes up with a minus eleven point nine
that’s negative again so that’s a miximum So under those, in this case you’d put a mountain
and if it’s a minimum you’d put a tiny valley
and after you find the x values of where it crosses the x axis
you are almost done with graphing that function pretty neat huh
everystepcalculus.com go to my site
enjoy my programs and pass calculus
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