00:01
Hi there, so for this problem, we have the situation that is shown in here.
00:08
Okay, then the information that we are given for the function y, which is equal to the function f of x, is that the second derivative of this is less than zero, this for x less than 2, and the function, the second derivative of this function, is greater than 0, that means positive, for x greater than 2.
00:39
And that the first derivative of this function at 2, that is equal to 0.
00:47
So first of all, let's determine what this tells us about the function.
00:52
Now, the first, we know that the second derivative tell us about the concavity of a function.
01:02
Now, if the second, the second derivative of a function is less than zero for some interval, then the function is concave down.
01:17
This concave down for x greater than 2.
01:21
And the other one, when it is positive, is then concave up.
01:31
Okay, this in this case for x greater than 2.
01:34
And the first derivative at some point equals to zero, that means that this is a critical point.
01:44
That means that the function is changing from decreasing to increase, increasing, or the other way around, from increasing to decreasing, okay? so let's see what of the options behave like this.
01:58
So, as you can see, we have four options in here.
02:02
Now, the first one is not, because, from infinity, from minus infinity to 2, the function is concave up...