00:01
We have the function, y equals square root of 1 plus x cubed.
00:09
And we want to find the equation of the tangent line to this function at the point to 3.
00:19
The first thing we should check is that if we plug in 2 for x, what do we get? we got 8.
00:24
1 plus 8 is 9, square root of that is 3.
00:27
So this point is in fact at the very least on the graph of the function.
00:32
Now, if we want the equation of a line, we need the slope and, or it is sufficient to have the slope and a point on the line.
00:43
And from there, we can use this one of these standard equations for the line, y minus y1 equals m x minus x1, where x1, y1 is the point on the line and m is the slope of the line.
01:00
Now, we already have a point on this tangent line because the tangent line at 2 -3 goes through the point -2 -3.
01:07
So the only thing that we need is the slope at the point -23, the slope of the tangent line, which is the derivative at x equals 2.
01:21
So what we should do is find the derivative of this function.
01:26
Now, this function is a composition of functions.
01:28
It has an inner function, 1 plus x cubed, and an outer function, square root of an input...