00:01
So in this question, we're trying to find the absolute maximum and absolute minimum value of the function, f of x, and my f of x here is 12 plus 4x minus x squared, and i'm on the closed interval from 0 to 5.
00:20
Now, the first thing i have to do is i have to find what are called my critical points, right? the places where my derivative is either zero or undefined.
00:31
So let's start by getting my derivative.
00:34
Let's start by getting my f prime of x.
00:38
In this case, my f prime of x is just 4 minus 2x.
00:45
Once i have my derivative, i'm going to set this equal to 0.
00:51
Solving 4 minus 2x equals 0 gives us 4 equals 2x, or x equals 2.
01:00
X equals 2 is my only critical number here.
01:06
Now, what do i do once i have my critical numbers? i take my critical number and my endpoints, 0 and 5, and i plug them back into the original function.
01:19
So i'm going to be evaluating f of 0, f of 2, and f of 5.
01:28
And let's see what comes out...