00:01
So as we look at this problem, defined as f of x equals 1 minus 2x minus x squared, with a c value of 4, the first thing that they ask you to do is to double check that this graph is 1 to 1.
00:19
Well, you can double check that it's 1 to 1 if you take the derivative of this.
00:24
Sorry, that was x cubed, which is important because if you take the derivative of this and get negative 2 minus 3x squared, what you want to do is make sure that this graph is always positive or always negative.
00:41
So in this case, it is always negative because the moment, you know, for any x value, the moment you square it, it's going to be a positive.
00:52
But then when you multiply by a negative, you know, you're going to get a negative minus another number.
01:02
How about this? i'll change it to plus another negative.
01:05
Will always give you a negative.
01:07
So what does that tell me is that this function is always decreasing, which confirms that it is one to one.
01:14
The other bit that you need to do is figure out, because they ask you to evaluate, how do they write it, the inverse derivative at x equals at four...