Calculus, Graphing, critical point, critical numbers, Calculus Problems, TI-89 Titanium


Uploaded by Tommynnnnn on 01.08.2012

Transcript:
So, this video is on critical points and critical numbers, with regard to graphing by hand in
calculus. Calculus one, or all through calculus I guess. Ahh Let’s get started. You press
second alpha on your calculator titanium. See this box here which turns black which
shows you that you can enter letters. And the code for my menu of course is I n d e
x, and then you have to press alpha to get back to numbers and parenthesis, and you’re
into my menu. My menu has many many things in it. Right now we’re talking about critical
points, so - were gonna go – uhm - to critical points. Pull up the program, and I tell you
to mark on your paper right away, on your test paper or whatever, ya know, a graph with
these, ahh all labeled in numbers so you can mark down whatever comes up in my program,
and then you can, ya know, connect the dots and have your graph completed - by hand. So
we’re going to enter a function, a from a test, we’re going to have to – for any
of these boxes that come up in my programs you have to add alpha – you have to press
alpha first – so we press alpha, and we’re going to put in x cubed minus six times x
squared, plus nine times x and plus two, and then press enter twice – and I show you
what you’ve entered, in case you want, made a mistake, you can go back and do it, you
press enter again, you can, ok or change it – I’m saying its ok – my programs also,
you can press the number before these what the choice is, you can scroll down, or and
then press enter, but you can also just press the number and it will go right to there.
So were at critical points, we want critical points in the menu, instead of scrolling we’re
going to just press three on the calculator – and – and I - discuss a critical points
and numbers in a blog in my web site, so check that out. Uhm, most tests, come up with, ask
you for critical points, and there’s a difference between critical numbers, critical points
– and I discuss that – here I put a little bit of information about it. Critical point
is really an xy point on the graph, and critical numbers are – are on the x axis, just what
the x value is – however – professors and tests I’ve seen – uhm – ah – you
know use both and – and it’s not correct, their different. Ahh, So – in critical numbers,
your gonna - you’re going to set the uhm, first derivative to zero, and then solve for
x – so we factor the first derivative, here, and we come up with the critical numbers – x
equals three or x equals one – that’s what you’d put down – You put everything
on your test, just like this. You can’t find the first derivative unless you put the
function down – then you find the first derivative – and go from there – uhm – I
do the – I find critical numbers and critical points on my programs – so – we add - we
take three – one of the critical numbers of three – and plug it into the first function
– three cubed, times, minus - six times three squared, plus nine times three, and
you write this on your paper and you come with two – y equals two - so the first critical
point is three and two – second one you plug in one for critical number into the primary
function, and come up with six – so the second critical point is one and six – and
then, it takes you back – you can find more parameters here, press one, you can get more
parameters, and go whatever you want – local maximum min – Intervals of increase decrease
– inflection point – what ever you need to complete the graph