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Numerade Educator

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Problem 25 Easy Difficulty

Find $ f $.

$ f"(x) = 20x^3 - 12x^2 + 6x $

Answer

$$
f(x)=x^{5}-x^{4}+x^{3}+c x+d
$$

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Video Transcript

So for this problem here we are given um F double prime of X. And we want to find F. So we have capital prime of X. Given to us by 20 X cubed the complete -12 x squared plus six X. We take the first anti derivative. So F prime of X. This is going to be equal to 20 X to the fourth over five. That's going to be four X. To the fourth minus 12 X. Cubed over three. So that's minus four X cubed plus six X squared over two. So it's gonna be three X squared. Then we find F. That's gonna give us four X. To the fifth over five. So we have 4/5 X to the 5th minus four X. To the fourth over four fascist X. To the fourth plus three X cubed over three. That's just going to be executed. Um And then we have to remember that here we had to add our plus C. So here it's gonna be plus C. X Plus D. So that would be how we show this whole thing. This is gonna be to the fourth over force. This would be five. Which makes this a one. This would be our final answer.