00:01
Okay, here's the graph, okay? so we're looking for the x -value where the f has a local minimum.
00:09
As you see, this is the derivative function.
00:13
So the function is, derivative values are negative and then positive here, okay? and then this is also positive, positive, positive, and these are negative.
00:28
So we know that this thing has, this function has two critical points, okay? right? what are those? when derivative is zero, x equals zero and x equals four.
00:43
So at x equals zero, we can also put into the first derivative test, zero to four.
00:51
Here's the first derivative, right? so the derivative is negative below zero and zero to four, it's positive and then it's negative again.
01:05
So the function is decreasing, increasing, and then decreasing again.
01:10
So this is your local min, okay, at x equals zero, and this is your local max at x equals four...