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