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Numerade Educator

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Problem 36 Medium Difficulty

Find $ f $.

$ f'(x) = (x + 1)/\sqrt{x} $, $ \quad f(1) = 5 $

Answer

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Video Transcript

So for this problem we are given the F prime of X is equal to X plus one. It's good, divided by the square root of acts. So based on that, we know that F of X is equal to. Um If we view this as X to the one half right here And then we distribute, we end up getting X to the 1/2 Times X. So that's X to the 3/2ves Plus X to the one House. So I'm interviewed in that way when I take the anti derivative because that's going to be much easier, it'll give me and 3/5 X to the 5/3 and then it'll give me plus two thirds X to the three house. If it's in mind now we have class C. And when X equals one, so we get three fist plus two thirds 3 50 plus two thirds is 1.26 repeating. Instead we get five. So that means that We have 5-. Yes. Does that mean c. is equal to five 0666666. Which gives us this value right here, they're finally answer