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

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