00:01
For this problem, we want to find the local maximum and minimum values of the function, 3x to the 4th minus 4x cubed minus 180x squared plus 7.
00:10
So the first thing you have to do is to find the derivative of f.
00:15
Now, f prime of x, that's equal to 12x cubed minus 12x squared minus 3 .60x.
00:26
And then we want to set this to 0 and solver x.
00:30
To find the critical numbers.
00:32
Setting this to zero, we have 12x cubed minus 12x squared minus 360 times x.
00:40
That's equal to 0.
00:41
We factor out a 12x.
00:43
We have 12x times x squared minus x minus 30.
00:49
That's equal to 0.
00:51
We can still factor out x squared minus x minus 30.
00:55
We'll have 12x times x minus 6 times x minus 6 times.
01:00
X plus 5 that's equal to 0.
01:03
We then set each factor to 0, we get x equals 0, 6, and negative 5...