00:01
In this problem, we will cover the tangent line of a function.
00:04
So to solve this problem, we must first find the tangent line equation of this function at the point 1 -1, and to do so, we must start by looking for the slope of a tangent line, and the slope requires us to find the derivative.
00:22
So i will write f -prime of 1 equals the limit, as x approaches 1 of f of x minus f of 1 over x minus 1 and this is going to be x squared minus 1 over x minus 1.
00:52
We know the top can be factored into x plus 1, x minus 1, and that's going to be all over x minus 1.
01:03
1, we see that the x minus 1s cancel out, and we are left with the limit as x approaches 1 of x plus 1.
01:15
And when we plug 1 in for x, we get that our slope is going to be 2.
01:21
So that's the slope of our tangent line, and we can now proceed to creating our tangent line equation.
01:28
So we know that in point slope form, the tangent line equation is going to be y minus f of 1 equals f prime of 1 times x minus 1...