Video Example: Critical Points for Graphing Program
Raw 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. 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
Video Example: Equation of a line program
Raw Transcript
Ah, this video is going to be on the equation of a line, with regards to my fabulous programs that I’ve programmed on the TI-89 calculator, and ah, these are pretty simple calculations, but it’s easy to forget how to do it. It’s nice to have a program to be able to do it. So, I’m going to clear the calculator here and we’re going to put in; 2nd Alpha, 2nd has to appear here, and then the alpha has to, to become darkened to go for the letters. And I have to put that in the entry line – I n d e x – and you will to if you buy the programs, ah alpha, it goes back to the number system, and then put the closed parentheses in, and press enter and we’re into the ah menu. You’ll notice there are many, many things on this menu. Definite integral, ahh derivatives, you know in algebra all of derivatives, ah transforming ah problems. Curl, product rule, quotient rule, whatever, but we’re going to do equation of a tangent line, you can press alpha e, or you can scroll down like this, and ahh, and press enter equation of a tangent line. Ah we’re going to enter the function, five times x squared, plus six times x, plus one let’s say – notice I forgot to press alpha, first, which is easy to do on this calculator, and so I’m gonna go back with two, I’m going to change it, and I’ll press alpha, five time x squared, plus six times x, plus one, and that’s better, five x squared plus six x plus one that’s the function – now say it’s ok – so we’re gonna, I generally press the one before the choice – and then we’re going to enter the x y component, you know, x, the values for x and y, so let’s do that now, let’s do it. You have to the parenthesis in first – you have to go alpha again – and put, let’s go three comma sixty-four, something – close out the parenthesis – and let’s see – now we got three, x y z equals three sixty four, that’s cool – press one – and we have the original function – we find the derivative of it, the slope – which equals ten x plus six – at three – our x choice that we had, is the derivative, derivative at three is ten, and then add the three to the x and there’s the – thirty six is the slope which is m – press enter again – shows you the formula – you write this stuff on your paper as you go – and at y equals sixty four – which was our choice – sixty four equals m x plus b, so sixty four equals thirty six that was the slope – times 3 – which was x – plus b, sixty four minus one o eight minus forty four – here’s the formula – y equals 36 s+ minus 44 – for that point- pretty neat, huh? everystepcalculus.com – check it out
Calculus and you
The difference in my programs as created for myself compared to other programs on the TI site or internet itself, is that the emphasis is on the mechanics, the perfect system, step by step, to a problem's solution. No theory, no proofs just be able to do the problem for my tests or homework and move on. If after that I wanted to know more about a problem, the whys and wheres etc. fine, but at least I could do the problem. You will learn with my programs as hundreds have for tests or homework but with no emphasis on theory, or proofs. In my experience in college there was no time for true learning or understanding, just cram, test and forget.I came to the unwanted experience at the age of 50 going to college for the first time, that college was teaching me everything I never wanted to know about things that made no difference. Like drinking from a fire hose. Too much material and no time. Enjoy my programs, Tom
Calculus I, II, & III
“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater”.
-Albert Einstein
Who am I?
Im the guy who went back to school like Rodney Dangerfield and wanted my degree in Electrical Engineering. It seems nowadays there is always one old person going back to college…I was that guy. I’m pretty smart but failed Calc I and had to retake it. The Ti calculator that was able to be programmed hadn’t come out yet during Calc. I. When it did in Calc. II – and I found out that it could be programmed – I was on my way and got A’s for Calc II and III (By the way, I Got an A for the Calc I retake also).