00:01
There's a lot happening in this problem, but i think we can attack this pretty nicely.
00:12
And what i'm going to do first is just the power rule, where what you do is you multiply the exponent by the coefficient, and that gives me negative 18, and you subtract one from the exponent, so i get two.
00:25
And then proceed, 27 times 2 is 54, just double checking x to the first, and then the derivative of a linear piece is just.
00:36
The coefficient and the derivative of a constant is zero.
00:40
So this would be the first derivative.
00:43
So then the second derivative is just the power rule again.
00:47
So now i'm at negative 36x minus 54.
00:51
Same rules just doing it a second time.
00:55
So now we're going back to the first derivative, which was what i hadn't read.
00:59
And i'd say that it's factorable.
01:01
Now i'm not sure, but i have a hunch that all those numbers are divisible by 18.
01:07
So i'm jumping to this and i'm factoring out in negative 18.
01:11
So i'm left at x squared plus, let's see, 54 divided by 18, makes it 3x, and then that becomes negative 18.
01:22
And now i can factor that to be 6 minus 3.
01:28
So the factors would be x plus 6, x minus 3, equal 0.
01:35
And then the solutions, or the critical values, i'll just write cb for that, are the opposite of those two.
01:43
So it would be negative 6 and positive 3...