Math  /  Calculus

Question21. Consider the function f(x)=x34xx3+1f(x)=\frac{x^{3}-4 x}{x^{3}+1}. (1) Find the domain, the xx - and yy-intercepts, (2) Find the asymptotes, (3) Find the intervals of increase and decrease. (Tip: The root for 8x3+3x24=08 x^{3}+3 x^{2}-4=0 is x0.68636x \approx 0.68636.)

Studdy Solution
Summarize the intervals of increase and decrease.
- f(x) f(x) is decreasing on (,1)(1,0.68636) (-\infty, -1) \cup (-1, 0.68636) . - f(x) f(x) is increasing on (0.68636,) (0.68636, \infty) .

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