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Numerade Educator

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Problem 44 Hard Difficulty

Find $ f $.

$ f"(x) = x^3 + \sinh x $, $ \quad f(0) = 1 $, $ \quad f(2) = 2.6 $

Answer

$$
f(x)=\frac{1}{20} x^{5}+\sinh (x)+1.81343 x+1
$$

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Video Transcript

The first problem here, what we have is F double prime of X is equal to X cube Plus, sign eight x. Um Then when we take a five X or F prime of X, that's going to give us X to the 4th over four class or minus person Ajax. Then what we have is This is uh since f prime of two is 2.6, what we end up getting as a result is one 81343. Oh right. It 1343. Then when we take f of f this is going to be X to the 5th over 20 bus, sign each X class. Um one point this whole thing X. And then we know when we plug in zero, we get one. So that means that our constant is just one, then this will be our final answer.