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Numerade Educator

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Problem 31 Medium Difficulty

Find $ f $.

$ f'(x) = 1 + 3\sqrt{x} $, $ \quad f(4) = 25 $

Answer

$$
f(x)=x+2 x^{3 / 2}+5
$$

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Video Transcript

Okay, so we're being asked to find Jeff, and we're given the condition of F Prime Vex IQ would want us to your ex and every forty was for five. So let's get right to it. I'm gonna be right after I'm back as one plus three extra one half Just make my integration a lot easier. So there's gonna be warned. Plus three x to one. The eggs. Well, that's just going to be X. And then plus three accident, one half plus one with us three half. So this will be excellent. Three half over three half, which is just too third. And I don't have a plus Constant c and this is this will be f the three year old cancels. So now we have an expression on eggs to act to the three half Go on Plus is equal under pussy. And now we're going to do a plug in for to get twenty five. So we put in effort for Well, then we get twenty five, three four plus two. Um, and then this will be for raised to the power of three half and let's see. And then effort for is equal to twenty five. So four plus two and four racial power three and take screwed. And that, well, that just give you time's A and plus See vehicles went by, Uh, so in terms of sixteen and then sixteen points for just twenty, so twenty plus C is equal to twenty five and C is equal to five. So that mean original function now was going to be, I mean, a new function. It's going to be after back people eggs plus to actually three half plus right, and that is our function.