00:01
In this question, we are asked to find the absolute maximum and the absolute minimum values of the given function.
00:06
And to do that, we first need to calculate f prime of x, and that's going to be 12x squared minus 24x, minus 36, and set it equal to 0.
00:22
And solve that equation.
00:24
Note that we can divide everything by 12.
00:26
We are going to get x squared minus 2x minus 3 equals 0.
00:34
And we can factor that as x minus 3 times x plus 1 equals 0.
00:44
That means that the solutions are x equals 3 and x equals to negative 1.
00:50
These are the critical points of our function.
00:59
Now, to find the absolute maximum minimum values, we need to evaluate the function at the end points of the interval and at the critical points.
01:09
So we need to calculate four numbers.
01:11
We need to calculate f of negative 2, we need to calculate f of 4, we need to calculate f of 3 and f of negative 1.
01:30
Well, we just need to plug in the given values in the function, in the original function.
01:45
So first we need to replace x by negative 2...
