00:01
All right, let's look at the information that we know that's given to us.
00:07
We have a function y equals f of x.
00:11
That is not the graph of f of x.
00:16
This blue line is actually the graph of the line that's tangent to the graph of f of x when x is 2.
00:27
So this line will be tangent to the graph of f of x when x is two.
00:34
Now, we don't know what f of x looks like, but here is x equals 2.
00:40
And we know that if we follow from 2 up until we hit the tangent line, let's draw a little point in here.
00:50
This point right here is where this tangent line is going to touch the first.
00:58
Function.
01:00
So this line is tangent to the function f of x when x is 2.
01:06
Now, we don't have the graph of f of x.
01:09
We don't know what it looks like, but we can draw something in just to try to help us out.
01:15
So let's see.
01:16
Let's use, i use this green color.
01:20
So if i want to draw in f of x, now if this line is tangent to the graph of f of x, is tangent to the curve of x, is tangent to the current.
01:30
Of f of x at this point that means you want the curve to kind of have the same slope well it has to have the same slope at this red point that the that the line does you want to try to draw the function so that it's so that it's tangent right there so let's let's go ahead and draw in the graph of what f of x might look like all right so this is what f of x might look like now you can see that this blue tangent line, here's the equation of that tangent line over here, but you can see that this blue tangent line is tangent to the curve right there at that red point.
02:17
So the slope of the green curve right at this red point is the same as the slope of that tangent line, that blue tangent line.
02:27
Now, we want to answer these two questions.
02:30
What is the value of our function f when x is two? well, the function when x is 2 will be the same point.
02:47
When x is 2, the function value and the tangent line have the same value.
02:54
So to make a long story short, when x is 2, you can see that the y coordinate for this red point is 3...