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Numerade Educator

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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)?

Answer

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

is this Probably require a calculator I'LL skip the detail our if you want to do with yourself which is quite lengthy, you you have to use So the general which the numerous are the denominator up it is and you have to beauty pride by that the river TV inside which there you have to compute it by using the kosher This is quite a lengthy So I'll give you i'll leave the details to you and the questions allow you to use a calculator for horizontal attention You simply solved the equation The relative equals zero and go from there.