Let . On which of the following interval sets is increasing? (Here…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let f(x)=x3−3xx2+1f(x)=\dfrac{x^{3}-3x}{x^{2}+1}. On which of the following interval sets is ff increasing? (Here a=−3+23 ≈0.681a=\sqrt{-3+2\sqrt3}\,\approx0.681.) (a) (−∞,−1)∪(1,∞)(-\infty,-1)\cup(1,\infty) (b) (−a,a)(-a,a) (c) (−∞,−a)∪(a,∞)(-\infty,-a)\cup(a,\infty) (d) (−∞,−3+23)∪(3+23,∞)(-\infty,-\sqrt{3+2\sqrt3})\cup(\sqrt{3+2\sqrt3},\infty)

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