00:01
Anytime you're asked to verify if a function is an anti -derivative, what you should do is just take the derivative of your answer.
00:12
So we're going to take the derivative of g prime, which is just your power rule.
00:17
Bring the two in front, two times two is four, and you subtract one from the exponent.
00:23
And when you see that that is equal to the original problem, then we can conclude, so this is the work, to conclude or verify that g is the anti -derivative of f.
00:38
So in part b, where they're asking you to come up with any correct anti -derivitum, you can label this whatever you want, because you don't want to call it g.
00:46
You could call it capital f.
00:48
It's actually kind of normal.
00:51
But as you learn how to do the anti -derivive, what you do is you add one to your exponent.
00:56
So this is x to the first.
00:58
Add one to your exponent, and you divide by your new exponent.
01:01
Divided by two gives me two.
01:03
But what you have to remember is that you need to add a constant to this.
01:08
Why? well, the derivative of a constant is always equal to zero...