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Numerade Educator

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Problem 38 Medium Difficulty

Find $ f $.

$ f'(t) = 3^t - 3/t $, $ \quad f(1) = 2 $, $ \quad f(-1) = 1 $

Answer

$\frac{=3^{t}}{\ln 3}$$-3 \ln t-0.7$

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Video Transcript

for this problem here, what we have is that F prime of X is equal to 3 to the T minus three Over Act So three of the Act -3 over X. So when we look at this, when we take the anti derivative, so F of X. That's going to give us the natural log. That's the US. 3 to the T mm Through the X over the natural log of three -3 times the natural log of the absolute value of X. So that right there is going to be our final answer. But then we have plus C. So when we use the initial conditions and plug in our value one, we end up getting too. So as a result, we know that it'll be plus or minus your 0.7. It's not right. There is going to be our final answer for the anti derivative of F prime of X.