00:01
We now determine the absolute extremo of the function f of x equals x squared minus 4x minus 6, define in the closed interval 0 comma 2.
00:10
So first we determine if there are any critical points in this interval.
00:16
So we find the critical point of the function by setting up this derivative equals 0, that is the first derivative equal 0 and solving for x.
00:27
So we find the derivative of f of x by.
00:30
Differentiating both sides with respect to x.
00:34
So we have f prime of x equals the derivative of x squared is 2x and we use the power root and the derivative of negative 4x is negative 4 times of the derivative of x is 1 and the derivative of negative 6 which is a constant is 0.
00:51
So basically we get f prime of x and this equals 2x minus 4.
00:57
Now we have to set up f prime of x equal to 0.
01:00
Now we have to set up and solve for x.
01:03
So therefore i replace f prime of x equal 0 and this gives 0 equals 2x minus 4.
01:11
And from this we can solve for x...