00:01
We're asked to find where the inverse is derivative, what that equals at the c value of negative 5.
00:09
Now before doing that, what we want to do is make sure that f of x has an inverse, and you can do that by finding the derivative of the function, 2x cube plus 2x.
00:26
So that's what i'm doing.
00:27
Just take the derivative, and it's just the power rule over and over again, or you multiply your exponent by its coefficient and subtract one from the exponent.
00:36
Now, the thing with this is it's always positive, because the moment you take a number to the fourth power, you get a positive.
00:44
The moment you square any number, you get a positive, or at least zero, and zero plus zero plus two gives you a number that is bigger than zero.
00:52
So if the derivative is positive, f is increasing, and therefore must be one to one.
01:06
So now what you need to do is think about that this is the x value of the inverse, so it's got to be the y value.
01:13
And what i do is i just guess and check.
01:17
And to me, a number that makes sense would be f of negative one.
01:22
I think that equals negative five, because the moment you take negative one to the fifth power, you get just five negatives so it stays negative...