00:01
We know the derivative of f of x is x plus one over the square root of x, and f of one is seven.
00:08
We want to figure out what f of x is.
00:12
I am going to rewrite our function.
00:17
The square root of x is the same thing as x to the one -half.
00:22
Now i'm going to rewrite this.
00:26
I could separate the top and make this x over x to the one -half plus one over x to the one -half.
00:40
In a matter of x to the first over x to the one -half, i just subtract the bottom power from the first and have x to the one -half.
00:48
And then the second one would be x to the negative one -half.
00:53
To find the function, i'm going to integrate the derivative.
01:00
So if i integrate x to the one -half plus x to the negative one -half, i have x to the three -halves power divided by three -halves, or times two -thirds, plus x to the positive one -half power, and i divide by a half or multiply by two...