00:01
Let f of x be the function whose graph is shown below, determine the derivative of f at 1, 2, 4 and 7.
00:11
So we have 1 here, then we have 2 right here, 4 right here and 7 here.
00:24
So let's see the derivative of f at 1.
00:30
So it's the derivative at this point right here.
00:36
You see that the function around number 1 is just a horizontal line.
00:44
That is, it is a function that is a linear function of degree 0.
00:54
It's a constant function.
00:56
So the function is constant from 0 to 3.
01:00
And the value is 1.
01:02
The function is constantly equal to 1 between 0 and 3.
01:08
For that reason, the derivative at any point on that interval is 0.
01:15
Because the derivative, remember, represents the slope of the tangent line to the graph at that point.
01:23
The tangent line to the graph of the function at any point between 0 and 3 is just the same function.
01:31
Because the function is a line.
01:34
And the slope of that line is 0 because it's a horizontal line.
01:39
So the derivative of 1 is 0.
01:41
And the derivative of 2 is 0 again because the same thing we explained before at this point.
01:48
So we have the tangent line is just the same function which is a line.
01:52
And the slope of that line is 0.
01:55
So let's see the other two.
01:57
The derivative at 4.
02:00
So we talk about the derivative around, at this point.
02:05
And we see the function, that interval from 3 to 5, is a line again.
02:11
But now, it's a line with some slope.
02:15
It's a positive slope.
02:17
What we know is that the derivative at this point, the tangent line, is just the same function again...