00:01
In this question, we are asked to find the absolute maximum and the absolute minimum functions of the values of the f over the interval, over the closed interval, negative 1 -4.
00:13
We call that the absolute maximum and the absolute minimum values can occur over a closed interval can occur only at the critical points, which are points where f -prime equals 0, or f -prime doesn't exist.
00:42
It can occur, they can occur at the endpoints.
00:48
In our case, there are x equals negative 1 and x equals 4.
00:54
First, let's find the critical points.
01:00
Using the chain rule, f -framm of x equals to 3 times x squared minus 1 squared times 2x equals 6x times x squared minus 1 squared.
01:19
Now we want this to be equal to 0.
01:27
We can divide everything by 6 and we can also rewrite x squared minus 1 as x minus 1 times x plus 1.
01:41
So the roots are x equals 0, x equals 1 and x equals negative 1.
01:51
And these are the critical points...