00:01
For this problem we are to sketch a function that is continuous and differentiable, and as the following properties, we have f -prime greater than 0 for x values in the open interval, negative 2 to 3, union 3 to positive infinity.
00:16
Its f -prime is less than 0 for x values in the open interval, negative infinity to negative 2.
00:23
F -prime of negative 2 equals f -prem of 3, and they're both equal to 0.
00:30
F of negative 2 is negative 1 while f of 3 equals 2.
00:35
Now when f prime is greater than 0, that means the function there by the first derivative test is increasing.
00:43
But if f prime is less than 0, our f is increasing in that interval.
00:49
If f prime equals 0, that means f has a horizontal asymptote at that x value, or that it can be a local max.
01:00
Or min.
01:01
And if f prime is not defined at a certain value, but f prime is defined, that means f as a sharp corner...