00:01
This problem says find the interval or intervals where the function is increasing and the intervals where it's decreasing.
00:06
And the function we're given is f of x equals 8 thirds x cubed plus 4 x squared minus 96 x minus 9.
00:13
And to figure out where we're increasing and decreasing, first we're going to find the first derivative of our function.
00:19
So that we can set that equal to zero to find where our possible extrema are.
00:23
And to find the derivative we'll bring down three and multiply by the coefficient, which would give us 24 thirds or 8.
00:29
And then we'll take one away from three for the exponent to give us 2.
00:32
We'll take the derivative here by bringing 2 to multiply by 4 to give us 8 and take one away from 2 to leave it as 8 x.
00:38
And the derivative of a linear term is just the coefficient and the derivative of our constant is zero.
00:44
So now we have our first derivative and we'll set this equal to zero again to find the possible locations of extrema.
00:51
Which is what we're looking for to help us find the increasing and decreasing intervals.
00:55
And to solve this we can factor out an 8 which will leave us with x squared plus x minus 12.
01:01
Now we're looking for two numbers that would multiply to be negative 12 and add to be 1...