00:01
Ok, so in this exercise we have our function f of x equal to negative 2x cubed minus 3x squared minus x plus 5.
00:11
Ok, let's find the derivative.
00:14
Well, the derivative is negative 6x squared minus 6x minus 1.
00:22
Perfect.
00:23
Now we need to study the sign of f prime.
00:27
How can we do this? well, we need to find the roots of this guy here.
00:34
Well, f prime of x is equal to 0 if and only if negative 6x squared minus 6x minus 1 is equal to 0.
00:45
So, if and only if, thanks to the quadratic formula, x is equal to 6 plus or minus square root of this guy squared, 36 minus 4 multiplied by 6.
01:02
So, minus 24 over negative 12.
01:06
Perfect.
01:08
So, what do we get? well, we get two roots, 6 plus square root of 12 over negative 12 and 6 minus square root of 12 over negative 12.
01:28
Perfect.
01:28
Ok, let me rewrite these two roots as negative 6 plus square root of 12 over 12.
01:44
And, well, this one is going to be negative 6 plus square root of 12 over 12...