00:01
In this video we want to find an equation of the tangent line to y equals x to the fourth plus one that is parallel to the line 32x minus y equals 15.
00:14
Okay so what we're going to do is we're going to let x naught y naught be a point on the curve y equals x to the fourth plus one.
00:26
We want to find the equation of the tangent line that is parallel to 32x minus y equals 15.
00:34
But if i solve for y, y equals 32x minus 15.
00:42
So in the first one we have 32x minus y equals 15.
00:46
If i solve for y i get 32x minus 15.
00:51
Now the first thing we need to do is get the slope of the tangent line.
00:56
If we want the slope of the tangent line we take the derivative of y equals x to the fourth plus one with respect to x and you'll see that you get 4x cubed.
01:08
Now if we take dy dx at x equals x naught that is equal to 4x naught to the third.
01:16
I just replaced x with x naught.
01:20
So the slope of the tangent line at x equals x naught is 4x naught cubed.
01:27
Now remember we want this tangent line to be parallel to y equals 32x minus 15.
01:35
But the slope of that line is 32 right? and parallel lines that are not vertical i might add have the same slope.
01:48
So what i'm going to do is i'm going to set 4x naught cubed equal to 32 because again we got the slope of the tangent line right? but if if we draw kind of a quick picture here, here's y here's x right? we have a curve...