00:03
All right, we're going to draw this function g, and here's what we know about it.
00:08
It's continuous on its domain negative 5 to 5.
00:12
That means when we draw it, it's never going to be past negative 5 on the left, past positive 5 on the right.
00:20
Do i have 10 here, 2, 4, so no.
00:23
Okay.
00:29
So here will be 1, 2, 3, 4, 5.
00:34
1, 2, 3, 4, minus 5.
00:38
Okay, so i can't go.
00:39
Past those doesn't have any holes or breaks in it because it's continuous.
00:45
Now the only point that they gave us is that g of 0 equals 1.
00:50
So i'm going to go to g of 0 on the x and 1 one on the y and i'm going to put a point.
01:00
Okay, however, we do know that g prime of 0 equals 1.
01:05
And what that means is this, at x equals zero, the slope of the tangent line to g is 1.
01:28
Because that's what the derivative means.
01:30
So i'm going to draw a dotted line, and it's going to be the tangent line, and a slope is going to be one.
01:37
So up one over one, up one over one.
01:48
Oops, went crazy there.
01:51
Okay, so when i draw the function, when it gets to that point, it has to just touch the tangent line and then go back.
02:03
Okay, how do i know it's underneath it? i don't.
02:06
Could be over on the other side.
02:07
It's okay.
02:09
All we got to do is make sure it goes to the point and that's tangent to that line.
02:14
Okay, now when we get to negative 2, it has to have a tangent of 0.
02:19
Okay, well, we're already to negative 2.
02:21
Let me erase just a little bit there.
02:28
Okay, when we get to negative 2, then we have to have a tangent line that has slope 0...