00:01
We will find the critical numbers of the function f of x equal 2x cubed minus 3x squared minus 36x.
00:14
So we remember that the numbers see in the domain of the function of the given function, such that the derivative at that point does not exist or exist and is equal to zero.
00:39
Are called the critical numbers.
00:42
So, numbers in the domain of the function, where the derivative does not exist or exist in an is equal zero.
00:51
So this is our definition here.
00:56
So the first thing we're going to notice here is that the domain of the function is, of this function here, is the real numbers.
01:05
Because it's a polynomial degree 3, so it is well defined everywhere in the real numbers.
01:11
So it's a main is the set of all the real numbers.
01:17
Following that, we find the derivative formula of the function and is 6x2 minus 6x minus 36.
01:29
And we know a polynomial has derivatives everywhere.
01:33
In fact, it's given by this formula, which is defined at all real numbers.
01:37
So the derivative of f exists at every real number x.
01:50
It means that we are not going to find critical points of this function.
01:57
That satisfies this condition of derivative not defined or not existent...