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Numerade Educator

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Problem 35 Hard Difficulty

Find $ f $.

$ f'(x) = 5x^{2/3} $, $ \quad f(8) = 21 $

Answer

$$
F(x)=3 x(5 / 3)-75
$$

Discussion

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Video Transcript

So we're told that F prime of X is equal to um crime of X rather is equal to five x. and the 2/3. Okay, so when we take the anti derivative of this, we end up getting X to the two thirds would become five thirds, So five x to the 5/3 divided by five thirds times 3/5 b three X to the five thirds. And then that's going to be plus some see value. We're told that F of eight is 21. So if you plugged in 8 to the 5/3, the 32 Free time fat is 96, So 96 and instead we're getting 21 so we would have to subtract this by 75, meaning that our final answer is F of X equals three X to the five thirds minus 75.