Transcript

Hello again everybody this is Tom from every step calculus.com every step physics.com. Calculus problem regarding a tangent line to a curve getting with two variables, I’m going to show you how that works on my programs, index 8 to get to my menu I’m already at equation of a tangent line here I’m going to enter the function you have to press alpha before you press anything in these entry lines, alpha x^3+6xy+y^2-8=0 you always have to transpose everything on the other side of the equation here and bring it over on the left side then make 0 to the right or a number to the right ether one would work, now because you enter y in here is going to be an implicit differentiation problem so here is the formula here that you just entered in the implicit system, it looks pretty good then click ok, differentiation both sides of equation with respect to x so here we go both sides and do each sides individually this one here because xy we need the product rule, you can write the product rule down and do it like this or you can just keep clicking and you will finally get to the product rule answer which is this right here which is (6+x) (dy/dx) and we keep going (2^y) = to the because it is a dy/dx also and you combine the functions dy/dx here and then no dy/dx just regular xy and the implicit answer is right here (-3*x ^2-6*y) divided by (6*x+2*y) now we are going to evaluate it at a point and the point is alpha 1 and alpha 1 so xy is 1 1 say its ok and we enter those variables into the numerator and the denominator come up with a slope of -9/8 slope of the line and then we figure the y=mx+b which is the slope m and the we add the one for the x and the one for the y and then figure out what b is here then you subtract this from one and one is of course 8/8 and when you subtract it you get 17/8 your subtracting a minus so you get 17/8 and here is the answer y=mx+b pretty neat, every step you go and I also give you the angle of the line the way it is pointing, if you notice the way it is pointing in this direction not up but down to the right and if you want to do it on a other points it will take you back there. Pretty neat ah, every step calculus.com go on my sight buy my programs if you want to pass calculus and subscribe if you want to see more videos that I might make. Hey have a good one.

x^3+6xy+y^2= 8

Raw Transcript
Hello again everybody. Tom from everystepcalculus.com and everystepphysics.com.
Calculus problem regarding a tangent line with a curve. Dealing with two variables. I show you how that works on my programs. Index 8 to get to my menu. I’m already at equation of a tangent line here to save time. And you’ll scroll down to it and then you’ll enter the function Alpha, you have to press alpha before you enter anything into these entry lines. Alpha x cubed plus 6 times x times y plus y squared minus 8 equals zero. You always have to transpose everything on the other side of the equation here and bring it over the left side and make zero on the right or a number on the right either one would work. Now because you’ve entered y in here this is going to be an implicit differentiation problem. So here’s the formula here that you just entered. In the implicit system. And it looks pretty good. I say it’s ok. Differentiate both sides of the equation with respect to x. So here we go both sides. We’re going to do each one individually. This one here because xy, we need the product rule. So you can write the product rule down and do it like this or you can just keep clicking and you’ll finally get to the product rule answer to which is this right here and 6x dy dx and we keep going. y squared is equal to this because it’s a y dy dx also. And you combine the functions, dy dx here and then no dy dx just regular X Y and the implicit answer is this right here minus 3x squared minus 6x, etc. Division sign here, you know. Now we’re going to evaluate it at a point and the point is alpha 1 and alpha 1. So xy is 11. I say it’s okay. We enter those variables into the numerator and the denominator, come up with a slope of minus 98. Slope of the line and then we figure that y equals mx plus b which is here is the slope, m, and then you add the 1 for the x and 1 for the y and then figure out what b is here. Subtract this from 1, 1 of course 8 eighths and you subtract you get 17 eighths. Subtracting a minus so you get 17 eighths. Here’s the answer y equals mx plus b. Pretty neat, huh? everystepcalclus.com you can go, and I also give you that angle of the line is pointing, notice that it’s pointing in this direction not up but down to the right and if you want to do it and other points, it’ll take you back there. Pretty neat, huh? everystepcalclus.com Go to my site, buy my programs if you want to pass calculus and subscribe if you want to see more videos that I might make you. Have a good one!

Equation to a Tangent Line Video Example

Below is a real test question from a student that we will solve and later graph it on a future post.

Equation to a Tangent Line: Raw Transcript

See how to graph the answer to this problem HERE

Hello this is Tom from every step calculus dot com
Going to show you how to do the equation to a tangent line
and a little bit about that I’m going to graph it for you too
have you maybe understand a little bit better even though we’re really
interested in passing our
tests and moving on never to touch calculus again
um, let’s get started you have to put index eight because of calculus one that’s in
my instructions
press Enter and
you notice this is the test problem actual test problem that was on a sheet
this person got nothing on this problem
where he could have probably got 20 points or ten
but its find the equation from the tangent to the curve of y=10x over
x squared plus one at the point 1 and 5 you’ll notice that this is a tough
question
also for calculus one in my opinion from professors it
should be calculus 2 or something because again you’re you’re having to do
the quotient rule notice you got 10x divided by x squared plus 1 so you
do the quotient rule first and then go to the
my program for equation of a tangent line
to figure out the equation for that y equals mx plus b
so let’s do that we’re going to we’re gonna gold scroll to
you have to know this stuff a little bit about calculus to be able to do the
programs but that’s okay
what we’re after here after the quotient rule
okay quotient rule scroll down the quotient rule
here it
is
write this down in your paper right very small nerds
write very small and sloppy because they are confident they know calculus and
and so that’s all of what they do
in my experience so anyways you notice you have to put again the
parenthesis with the division sign between and so we have two functions
where going to press alpha first to get to the so we can put the
function in my entry lines here
so we’re gonna put
0:00
parenthesis, we’re going to put the parenthesis
10 times x
close off the parentheses
divided by parentheses
X squared
plus one
close off that parenthesis show you what you’ve entered again
there’s f of x equals 10 of x g(x) equals
x squared plus one and we do the computations
write this on your paper so you look like a genius
and here’s the answer
10-10x squared over x squared plus one squared
okay notice that the quotient rule will always has an x squared or
square in the bottom in the denominator
so now we’ve got that in our paper now we need to go
to the main menu the answers number two
and we need to scroll to equation of a tangent line
you need to practice with my programs a little bit to
understand the menu and stuff and we go to equation tangent line
and we’re gonna enter our function
alpha again
10 times x
just an ordinary function add it like you would
into the calculator you don’t need parenthesis like we did to get the quotient rule or
the product rule divided by, of course division always needs a
needs a parenthesis in the in the denominator
that’s x squared
plus 1
and I show you what you’ve entered and they’re asking us to find the
equation to a tangent line at point 1
X they give you a .5 but that’s really nonsense because the
to do the equation gives you the that point which I’ll show you in a second
so we put alpha 1 and I ask if you
made a mistake on that we say it’s okay and so here’s the
slope of course of a tangent line, or slope of a line in the…
is a derivative of the function that’s all it is
it’s all I’ve ever figured out it is, so, It’s the slope of a line here it is if you add an
X value to it which we will do in a second which is one your gonna come up with a
certain amount
for y and so here’s the
here’s the first derivative and X equals 1 notice I put the one here
f of prime of 1 and then you’re gonna enter one in all these places were
x was you write that on your paper you generally put
parenthesis around here but I couldn’t do that in the programming so I had to put
quotation marks
to make it work and you come up with the slope of
0 m equals 0 so now x equals one we need to find out what
what y would be so we
put that into the original function and turns out y is equal
to 5 which is what they told you in the first place x and y is equal to 1 and 5
now we figure out the equation
and if y equals five then y equals mx plus b
five equals mx plus b and 5 equals, there’s the slope
m which is 0 and here’s X which is 1
and we’re gonna find what b, b is equal to 5 minus
0 equals 5 so the equations of tangent line is y equals
0x plus 5
um….pretty neat

Raw Transcript

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

Equation of Tangent Line to a Curve

Raw Transcript

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 you made 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