For the function

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For the function r(x)=x3−4xx2+1r(x)=\dfrac{x^{3}-4x}{x^{2}+1}, at which xx-values does the graph of rr have a horizontal tangent line? (a) x=±7+652x=\pm\sqrt{\dfrac{7+\sqrt{65}}{2}} (b) x=±−7+652x=\pm\sqrt{\dfrac{-7+\sqrt{65}}{2}} (c) x=±23x=\pm\dfrac{2}{\sqrt{3}} (d) x=−7+652x=\dfrac{-7+\sqrt{65}}{2}

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