The curve is defined for by and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The curve is defined for −2<t<2-2<t<2 by x=t2+1x=t^{2}+1 and y=t3−ty=t^{3}-t. For which values of tt is yy increasing with respect to xx? (a) −13<t<0 and 13<t<2-\dfrac{1}{\sqrt{3}}<t<0\text{ and }\dfrac{1}{\sqrt{3}}<t<2 (b) −2<t<−13 and 13<t<2-2<t<-\dfrac{1}{\sqrt{3}}\text{ and }\dfrac{1}{\sqrt{3}}<t<2 (c) 13<t<2\dfrac{1}{\sqrt{3}}<t<2 (d) −2<t<−13 and 0<t<13-2<t<-\dfrac{1}{\sqrt{3}}\text{ and }0<t<\dfrac{1}{\sqrt{3}}

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