Hello everybody this is Tom from everystepcalculuseverystepphysic.com. We are going to do a maximum and minimum problem in graphing functions index eight to get to my menu we’re going to scroll down here to local max and min there is it there you can do all these things after you put the function in I always tell you to start on graph paper because when you have a test you are supposed to find these things through derivatives etc. then graph it by hand on a peace of paper, so you find the points and continue to graph it so we are going to enter the functions we have to press alpha before you enter anything in these entry lines here, alpha function 6*x^3-9*x^2+8 it’s going to show you what you have entered and you can change it if you want, say it’s okay and then we are going to scroll down here to local max and min and we are going to wait for it to load, this is busy when it’s loading the program, it only does that when your doing it for the first time you load it and the rest of the time it is very quick and first we find the first derivative and then we say it is equal to zero and factor it and then find the x values x= 0 or x=1 theses are critical numbers alone the x-axis they are not critical points, critical point is when you put theses into toe original functions then solve for y and you get the y value and that’s a point and we’ve done that here and (x,y) = (0,8), (x,y) = (1,5) these are the points, very important and a lot of professors don’t make that clear and then to find whether it’s a max or min you put the critical numbers into the second derivatives and if the answer is negative then you know you have a maximum and if the answer is a positive then it’s minimum, you notice that they are opposite positive minimum, negative maximum, so we find the second derivative here it is here put x=0 in for that we get -18, -18 means it’s a maximum now notice this is a positive and therefore it is a minimum, now I graph this for you so you can see exactly what is happening and you can see here at 0,8 we have a maximum at 1,5 we have a minimum. Pretty neat huh, everystepcalculus.com go on my site buy my programs pass calculus, have a good one bye bye.

## Local Max and Min | Extrema on the TI-89 | Every Step Calculus Video

### 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