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Archives for June 2012
Graphing: Maximum & Minimum Program
Video Example: Critical Points for Graphing Program
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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
Equation of Tangent Line to a Curve Program
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This video is gonna be on the equation of a tangent to the x point on a curve. This is the line when you have found the first derivative and you find the slope. This is the equation that is in the line at the point where you find the slope. This program I pretty neat, check it out on my website. Turn calculator on and clear screen to get to the menu of the program by pressing F1 8. Now add index 8 () to get to the menu of the program. Press 2nd Alpha, enter index, press alpha again to get back numbers and parentheses add 8 (). Here we are, select the equation of a tangent line, scroll down and press enter. It shows you what programs are added here. Enter the function 8*x to the 3rd power + 6*x+9
You can change or press ok if you want. Now you want a point, maybe at point 3, press Alpha 3 (it shows x=3). If youmade a mistake you can change it or say ok.
Function: F (x) = 8*x^3+6*x+9
F (x) = slope
= 24*x^2+6
The derivative o 6x is 6 f’ (x) =24*x^2+6
@ x= 3
F’ (3) = 24*”3”^2+6
=222
You have to go back and put 3 in the function to find y
Y = f (x) = 5s^2+6x+9
@ x = 3
Y = 8*’3”^3+6*”3”+9
=243
So (x,y) = (3,243)
Y=243 (222 is the slope)
243 = mx+b
243= 222(3) +b
B=243-666
=-423
Y = 222x+-423
Video Example: Equation of a line program
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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
Natural Log Program
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Quotient Rule Step by Step
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Product Rule Step by Step
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so i’m going to demonstrate the uh… product rule on the titanium written you know with regard to my program start program a calculator uh… and to we need to get to the home screen here and you type index that i’m gonna clear this out and reapply it so they can show you how to do that you go second alpha get that little dark mark in there to show you you’re gonna put letters in the calculator i_n_d_e x and then alpha again to switch the numbers in parentheses and your into my programs there’s a menu of many many things depending on what i want to put in there but you know product rule like this one chain rule, quotient rule, quotient um difference quotient, limits trig integrals, derivatives log of base a or you know natural log derivatives, derivatives of thosebut anyways, we’re going to go team also goes straight up and then you can scroll down to go here’s velocity and stuff that you would need in calculus, um a lot of it were going to do the quotient rule in the next video but anyways were going to do the product rule now you can see that I’ve highlighted that, while that’s loading the formula for the product rule is of course h of x because you’re doing two functions f of x and g of x h prime of x is this uh… formula here prime of x g event epa vexed times g prime objectives the part of it for the and then were going to enter in the parentheses like this country an example so we have to go alpha and then enter the first parentheses and then you can enter whatever let’s do 5 times x squared plus six closed parentheses without the prince of sleaze which shows you what you’d entered the program you write that down in your paper dash if you think you want it if it’s okay if you like if you made a mistake and go back and change it whatever so saying it’s ok so each prime although it had to be good at wildness times the either function plus the other function times riveted the other functions of that so you write that on your paper ten x etcetera etcetera we come to the three h primal inferences that explicitly plus the derivatives at this when you add it up or multiply it up at forty-five expert ninety extra eighteen and that’s the product rule opt regarding my programs check them out of my website at least of calculus dot com
Chain Rule Program Step by Step
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