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Numerade Educator

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Problem 42 Hard Difficulty

Find $ f $.

$ f"(t) = t^2 + 1/t^2 $, $ \quad t > 0 $, $ \quad f(2) = 3 $, $ \quad f'(1) = 2 $

Answer

$$
f(t)=\frac{t^{4}}{12}-\ln (t)+\frac{8}{3} t-2.97
$$

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Video Transcript

So we're given that F double crime X is equal to X squared plus one over expert. What can we expect the negative too. Then we have that the F prime of X is going to end up giving us X cubed over three minus X, the -1 or -1 over X. Then that's me plus C. But we know that when X is equal to one, we'll end up getting to start going to give us uh eight thirds, then F of X, We'll end up giving us X to the 4th over 12 minus the natural log of X Plus 8/3 acts. And then when we have plus C and we evaluate it, we end up getting a negative 2.97. So that's our final answer.