The path of a roller-coaster loop is modeled by

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

Problem

The path of a roller-coaster loop is modeled by xtan⁡y−y2=0x\tan y-y^{2}=0, where xx and yy are measured in meters. Determine dydx\dfrac{dy}{dx} when y=π4y=\dfrac{\pi}{4}. (a) −4π(π−4)-\dfrac{4}{\pi(\pi-4)} (b) 8π(π−4)\dfrac{8}{\pi(\pi-4)} (c) −8π(π−4)-\dfrac{8}{\pi(\pi-4)} (d) −8π(π+4)-\dfrac{8}{\pi(\pi+4)}

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