00:01
To do this problem, let's start off with what we are given.
00:05
So the first thing we're given is f of x.
00:09
Now, this is a curve that we don't know the equation to, but for the sake of this problem, we actually don't need to.
00:16
The second thing they give us is the equation, y equals 4x minus 5.
00:22
Now, y is the tangent line to f of x at a equals 2.
00:30
Now, a is a value of x.
00:34
So what we're doing in this problem is that we're evaluating the tangent line of f of x at x equals 2.
00:42
And the task of the problem is to find the values of f of 2 and f prime of 2.
00:52
Now to solve this, we first need to understand how tangent lines work.
00:58
To do that, let's look at an example.
01:00
Let's say we have a random curve here and we'll call it g of x.
01:07
And let's say this point on the graph is point c.
01:13
So let's say we want to find the tangent line of g of x at c.
01:18
So what we're going to do is first we'll start at g of c and then the tangent line is going to look something like this.
01:32
So with this tangent line, we can make two observations.
01:36
Let's call the tangent line w.
01:40
So the tangent line is w and the curve is g of x.
01:44
The first observation that we can make is at x equals c, w equals g of x.
01:54
So what do i mean by that? if we look at the point x equals c, we notice that w and g of x are the same...