00:01
Okay, so for this question, we're going to be using the first derivative test.
00:05
Here are a little bit more about this function.
00:07
First for friday, it asks us to find the critical points.
00:10
So to do this, we're going to take the first derivative.
00:14
That'll be using the power rule 3x squared minus 12x, and the derivative a constant is 0.
00:22
So now we're going to set this equal to 0, because the critical points is when the derivative equals 0.
00:31
Doing a little algebra here, we can factor out an x.
00:35
And here we find that x equals 0 and x equals 4 make this equation true so these are our critical points now for part b it asks us to find when the function is increasing and decreasing so this is when we're going to use the first derivative test to predict what's going to happen so we're going to go ahead and plug in a negative 1 which is just before the first critical point we're going to plug it into the first derivative so doing this we get 3 plus a 12 so it's going to be greater than 0.
01:09
So we know that if this is 0, x equals 0, we know that it's going to be increasing before then.
01:17
Now we're going to test after the critical point of x equals 0, so we'll try 1.
01:24
And here we'll get 3 minus 12.
01:26
So the derivative will be less than 0, so we know that it decreases after 0...