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Numerade Educator



Problem 92 Hard Difficulty

(a) Use a CAS lo differentiate the function
$ f(x) = \sqrt \frac {x^4 - x +1}{x^4 + x +1} $
and to simplify the result.
(b) Where does the graph of $ f $ have horizontal tangents?
(c) Graph $ f $ and $ f' $ on the same screen. Are the graphs consistent with your answer to part (b)?


a. $\frac{3 x^{4}-1}{\sqrt{\frac{x^{4}-x+1}{x^{4}+x+1}}\left(x^{4}+x+1\right)^{2}}$
b. $x=\pm \sqrt[4]{\frac{1}{3}}$
c. $x=\pm 1 / \sqrt[4]{3}$


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Video Transcript

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