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Numerade Educator

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Problem 41 Medium Difficulty

Find $ f'(x) $. Compare the graphs of $ f $ and $ f' $ and use them to explain why your answer is reasonable.
$ f(x) = x^4 - 2x^3 + x^2 $

Answer

$$f^{\prime}(x)=4 x^{3}-6 x^{2}+2 x$$

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Video Transcript

he has cleared. So when you right here. So we have our original, and we're gonna find our derivatives, which is equal to X the fourth minus two ex cute bliss X square. Take the derivative. When we get for X Cube minus six X square close to acts, we're gonna graph it our original I'm gonna do in black and are derivative Odd zoo in red. So we have thio Note that are derivative is positive when the originals increasing and negative When the original is decreasing And whenever FF X is at a local minimum or max the derivative is equal to zero.