00:01
Okay, so we want to find the equation of the tangent line given our following function and our point.
00:07
So in order to find our tangent line, we need to find our slope.
00:12
And this equation here gives us our slope.
00:16
So we'll start by finding that.
00:18
So we have f prime at c, where c is our x point.
00:22
So we have an x of 1.
00:24
So that's equal to the limit as x approaches 1 of our following function.
00:32
3x or 3 minus x squared and then minus the function evaluated at 1 so that's 3 minus 1 which is 2 and this is all over x minus 1 so let's simplify what we have this is the limit as x approaches 1 of this would be negative x squared plus 1 over x minus 1 and now let's notice that our numerator is just a difference of 2 squares we can rewrite this as 1 minus x and 1 plus x.
01:26
Ok, so let's pull out a negative value from this term here.
01:31
So we can rewrite this as the negative of x minus 1, and then we can cancel this term with this one...