00:01
We're asked to plot x minus 3 to the fourth power.
00:05
Clearly that is 0 when x is 3.
00:07
We can also see that because it's raised to the even power, it's always going to be positive.
00:13
So we know that it's never going to, the minimum value that it's ever going to take is zero.
00:18
So this is going to be a local or a global maximum or minimum.
00:23
So we'll see that in a second.
00:25
Now we can see that there is symmetry here, but it's not symmetry about the y -axis here.
00:31
So this isn't an even function.
00:32
But if we shifted the y -axis, if we set x -bar equal x -minus 3, then we would have x -bar to the fourth as our function.
00:41
And then that would have symmetry about the new y -axis.
00:45
But this isn't even because it has symmetry about this axis about x equals 3.
00:51
But it's not an even function in the classical sense of the word.
00:56
We could change coordinates to make it an even function.
01:01
Taking a derivative, we get four x -minus three...