00:01
The underlying theme on this is if you have a horizontal tangent, that basically we're saying, i want to use the same notation, because they're talking about y equals, then dy, dx, at certain x values, may i only even say at x equals c, must have the equation of the derivative should equal zero somewhere.
00:30
And usually there's a little space there.
00:32
Sorry about that.
00:33
That's the overall premise of this problem.
00:36
So what we need to do is, first of all, write out the equation 2x cubed.
00:43
But then what i'm going to do is find the derivative of this.
00:53
So, d, y, d, x, would equal 6, because you bring that 3 in front times 2 is 6, x squared minus 54.
01:05
And we're going to set that equal to zero.
01:08
So now what i can do is add 54 over and divide by 6 to solve for x squared.
01:17
But i would simplify that because both those numbers are divisible by, i think, by 6, right? you would get 9...