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Numerade Educator

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Problem 28 Easy Difficulty

Find $ f $.

$ f"(x) = 1/x^2 $

Answer

$$
f(x)=-\ln (x)+c x+d
$$

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Video Transcript

So here for this problem were given F double prime of X to be equal to one over X squared. And I'm gonna write that as X to the negative too. Then I'll make it simpler for us in the long run, that tells us that F prime of X is going to be X to the negative one over a negative one, which is just negative one over Acts plus C. That tells us that F of X is going to be equal to negative the anti derivative of one over X is actually going to be the natural log of the absolute value of X. So then based on that, what we end up having is um plus C. X. Class D. Um And the reason why we have plus six is because this is some constant. So it's anti derivative of B plus C X. And then we have plus D. For the final general constant.