00:01
They want us to find the equation of the tangent line for y is equal to 4x minus 3x squared at the point to negative 4.
00:09
Well, the first thing we'll need to find out is what the slope of our tangent line will be.
00:14
And remember, we can get that slope by doing the limit as x approaches 2 of f of x, f minus 2, all over x minus 2.
00:29
Using this equation since our x value we're interested in is at 2.
00:34
So let's go ahead and first figure out what f of 2 is.
00:37
Or actually they already tell us it's negative 4.
00:41
Now let's just plug everything in.
00:44
So we're going to have the limit as x approaches 2 of, and then f of x was 4x minus 3x squared minus 4, all over x minus or actually it's minus minus four and then we have x minus two in the denominator so we can rewrite this as the limit as x approaches to of and i'll write this in ascending order 3x squared plus 4x plus 4 all over x minus 2 now if we were to plug 2 in now we'd get 0 over 0 so why don't we go ahead and divide these and i'll do this division synthetically.
01:34
So the b2 divided by, so let's see...