00:01
For this problem we're given, the revenue function, which is in $1 ,000, that's equal to 9 over 16 times, negative x cubed plus 51x squared plus 150x minus 500.
00:13
For x in the close interval, 0 to 25, where x is in $1 ,000, and x is the amount of, or the amount spent on advertising.
00:25
And here we want to find the point of diminishing returns.
00:28
The point of diminishing returns is the point at which the second derivative is equal to 0.
00:36
Now, r prime of x, that's equal to 9 over 16 times negative 3x squared plus, 51 times 2, that's 1002x plus 150.
00:50
So the second derivative r double prime of x, that's equal to 9 over 16 times negative 6x plus 100.
00:59
And 2...