00:02
Hi, in this video we're given that the total number of movie tickets sold since a movie's release is given by this function t of x is equal to 120 x squared over x squared plus 4.
00:22
And so the question is how fast are the total receipts changing one year, five years, and eight years after its release.
00:29
So all this is asking for is t prime of 1, 2 prime of 5, and t prime of 8.
00:45
So first we need to figure out what t prime is.
00:51
So i'll do that down here.
00:59
So because t of x is a quotient, we need to use the quotable.
01:04
So to do that, we take the bottom times the derivative of the top, which is 240x, minus the top, 120x squared.
01:15
Times the derivative of the bottom, 240, all divided by x squared plus 4.
01:26
And then we can try to simplify this, so we have 240x cubed plus 890960x minus 240x cubed.
01:42
Those will cancel.
01:44
Oh, and sorry, this should have been squared down here over x squared plus 4 squared.
01:54
So we can leave it like this.
02:01
Okay, and so now we just have to plug in these numbers...