00:01
Today, we'll be finding the equation of a line that is tangent to the curve x cubed minus 3x plus 1 at the point 2 .3.
00:09
I already have the equation that we will use written out.
00:11
It's the limit as x approaches a of f of f minus f of a, all divided by x minus a.
00:17
So we'll start by plugging in values for the equation.
00:21
We have the limit as, sorry, limit as x approaches to, f of x, in this case, is, is x cubed minus 3x plus 1.
00:35
And f of a, we will plug in 2 for a, because 2 is a.
00:39
2 cubed minus 3 times 2 plus 1, all divided by x minus 2.
00:50
Simplifying a little bit, we have the limit as x approaches 2.
00:54
X cubed minus 3x plus 1, minus 8, plus 6 minus 1, all divided by x minus 2 and simplifying a little bit more.
01:09
We'll have the limit as x approach is 2 of x cubed minus 3x, the plus 1 and minus 1 cancel out, and negative 8 plus 6 is negative 2, all about it by x minus 2.
01:21
I'm going to move over to the side to a factor x cubed minus 3x minus 2.
01:26
Using the rational root theorem, x plus 1 is a factor of this...