00:01
Our task is to find the inverse's derivative at the c value of 2.
00:11
So there's a couple of things that you need to do first, and that's to make sure that the derivative does exist.
00:18
And i appreciate that they went ahead and changed this.
00:22
Well, let me change this to something that's easier for me.
00:26
But they also give this notation that x needs to be greater than zero, which is helpful because when you take the derivative of this, you know, it's just three and do the power rule.
00:39
Negative 3 times negative 3 is positive 3, x to the negative 4th power, or in other words, 3 plus 3 over x to the 4th.
00:48
And considering that x is greater than 0, now this number is always positive, so it's always increasing.
00:55
If the derivative is positive, f is increasing.
01:00
But it's helpful because we can ignore when x is 0, when the function is undefined, and also on the chance that, you know, it still fails a horizontal line test.
01:12
So this one is still good.
01:15
So therefore, the graph is one to one and the inverse exists.
01:20
So i think i need to circle this as well as what the final answer is...