00:01
Alright, so given the function as h of x equal to x cubed minus 5x squared and minus 2x, let's find the derivative of that.
00:19
So we're going to have 3x squared minus 10x minus 2.
00:27
So using the ac method, values that we multiply to 6.
00:36
So actually there's no value that we multiply to 6, that also gets us to 10.
00:41
So let's use the quadratic equation.
00:44
So we're going to have x equal 10 plus or minus the square root of 100 minus 4 times 3 times negative 2, all over 2 times 3.
01:00
So that's 10 plus or minus the square root of, that's 100 plus 24.
01:07
So 124 over 6.
01:11
So if we simplify those terms, we'll have 10 plus the square root of 124 over 6 is going to give us 5 plus the square root of 31 over 3.
01:31
So those values are going to be 3 .522.
01:43
And then if we subtract that number, then our other value would be negative 0 .189.
01:55
So let's find those, let's plot those on the number line between negative 2 and 10, negative 0 .189 and 3 .522.
02:17
So let's choose these numbers like 0 and then negative 1 and then 4.
02:26
So when we throw in negative 1 into our first derivative, we'll get 3 plus 10 minus 2.
02:35
So that's going to give us a positive number...