00:01
Okay, they want you to take the derivative of f of x equals the absolute value of 1 plus x squared.
00:07
Well, x squared is always zero or positive, and when you add it to 1, it's always greater than 1.
00:15
So these absolute values are doing nothing here.
00:19
Okay, and so then the derivative would be 2x.
00:27
All right, let's see if we believe it.
00:29
Okay, 1 plus x squared looks like this.
00:35
And so when you take its absolute value, it still looks like that.
00:38
And so over here, the slope is negative.
00:41
And up here, the slope over on this side, the slope is positive.
00:45
Okay, so i'm wondering if maybe you typed in the problem wrong, and maybe you meant the absolute value of 1 minus x squared.
00:51
It's much trickier, okay, because it looks like this without the absolute value, 1 minus x squared, because it's an upside -down parabola shifted up 1.
01:04
So when you take the absolute value of it, okay, this part stays the same because it's already above the x -axis, and then the part that's below flips around and goes like this.
01:17
Okay, it comes up like that and up like that.
01:22
Okay, so what you have to do is you have to write this as a piecewise function.
01:28
So between, this is minus one and one.
01:31
Between minus one and one, you really do have one minus x squared.
01:39
Okay, then for numbers bigger than one, or, or for numbers less than minus 1, you get the opposite of what you had before.
01:46
So the opposite of 1 minus x squared for x less than minus 1, and the opposite of 1 minus x squared for x bigger than positive 1...