Problem 82E

82. (a) Use a CAS to 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 $f^{\prime}$ on the same screen. Are the graphs consistent with your answer to part (b)?

Step-by-Step Solution