00:01
So we're given the function f of x equals 4x squared minus 3, and we're asked to find the slope of the, we're asked to find the equation of the tangent line to the curve at the point negative 1 comma 1.
00:14
And so to do that, first we need to find the slope.
00:17
And so the slope of the tangent line is going to be given by f prime of negative 1.
00:22
And we have to find f prime of negative 1 using the limit definition of a derivative.
00:28
And so to find the derivative of a function at a point that's going to be equal to the limit as x approaches a of f of x minus f of a divided by x minus a.
00:41
And so first we want to find f prime of negative 1.
00:45
Remember that.
00:45
This does not give us the equation.
00:47
This gives us the slope of the tangent line at the point.
00:50
And so f prime of negative 1 is going to be equal to the limit as x approaches negative 1 of f of x minus f of negative 1 divided by x plus 1.
01:07
And so f prime of negative 1 is going to be equal to the limit as x approaches negative 1 of f of x, which is just our function minus f of negative 1 divided by x plus 1.
01:28
And so now we, if we direct substitute x equals negative 1 into this expression right over here, we're going to get 0 over 0...