0:00
Great.
00:01
So this problem asks us to take the derivative, or not take the derivative, we do need to eventually.
00:08
This question asks us to find the slope of the, or to find the equation to the tangent line of this curve, y equals e to the 2x, that passes through the origin.
00:17
This is the origin here, 0 .0.
00:20
So the idea here is we're going to take the derivative of this function.
00:26
We're going to come up with the equation to the tangent line that passes through 0 -0 in general.
00:31
Where the derivative is e to the 2x.
00:34
And then we're going to set that equal to the function itself.
00:39
So then we can verify that we can find the x value, or we can find the slope that we need for this tangent line.
00:49
So the idea here is first we're going to take the derivative, right? y prime equals as kind of a big prime to e to the 2x, right? okay.
01:02
Then we're going to say, we'll set this up as follows.
01:06
We'll say, well, our tangent line is y minus y, 0, which is 0, equals the slope, which is, it's going to look a little bit weird here, but we're going to do this in general.
01:20
It's going to be 2e to the 2, and then whichever point it is, i'm going to call it t.
01:30
And maybe i'll draw a picture to have this make a little bit more sense, x minus x0, which is zero.
01:36
The idea here is we need to find, we have our function here, right? here's our point of origin, right? and we have the slope for any line, so we're trying to find this point so that the tangent line, so there's the tangent line, right? and we already know this point, and we want to find kind of this point, which should give us the slope.
02:10
So, and that's going to be, this point here is going to be t, comma, y of t here.
02:23
Or e to the 2t, i guess.
02:33
E to the 2t.
02:37
Sorry about the color change there, but you get the idea.
02:40
Cool.
02:41
So, how are we going to do this? we got this thing here.
02:46
We can simplify this...