00:02
So the answer to this one is the third one, which is that f has local extreme at x equals 0 and x equal three halves.
00:10
And the point is that if you look at f of x, this is going to be 2x cubed minus x to the fourth.
00:26
So f prime of x is equal to 8x squared minus, uh, not eight, six x squared.
00:40
Minus 4x cubed.
00:46
So to find critical points, you have to set it equal to 0.
00:50
So you get f prime of x equals 0, which implies that, let's see, 6x squared minus 4x cubed is equal to 0, which then you can factor.
01:08
So you get 6 minus 4x is equal to 0.
01:12
So you get that the critical points are x equals 0 and x is equal to three halves, right? but these are critical points and not necessarily local extrema...