00:01
We're starting with g of x, and we're asked to verify that this function is the correct anti -derivative of f of x.
00:11
And how we want to do that is just to take the derivative of this function.
00:16
So the derivative of g, if you remember the power rule, you just bring the three in front and multiply by one -third.
00:21
So it would be one, which you don't have to write down the one, because one times anything is just that thing.
00:28
And then subtract one from the exponent.
00:31
And that is equal to f of x.
00:34
So you're verifying that the derivative that you found up here, and maybe i need to write out the correct, i don't know if anybody really needs to see this, but the derivative of x to the n power is equal to n x to the n minus 1.
00:50
So if we're working backwards for part b, for any function you want, you want to do the opposite.
00:59
So instead of subtracting one from the exponent, you want to add one to the exponent, and instead of multiplying by the old exponent, you want to divide by the new exponent.
01:11
And if you notice it is the same thing as what's up here, the only thing that's missing is plus c.
01:15
If you're curious why we need a plus c, is because we could have any constant, and when i take the derivative, would be zero...