For the curve defined implicitly by

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

Problem

For the curve defined implicitly by x2+y2=25x^{2}+y^{2}=25, what is the value of d2ydx2\dfrac{d^{2}y}{dx^{2}} at the point (3,4)(3,4)? (a) −2527-\dfrac{25}{27} (b) 2564\dfrac{25}{64} (c) −2564-\dfrac{25}{64} (d) −2516-\dfrac{25}{16}

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