For the curve

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

Problem

For the curve

x^{2}y-y^{3}+4=0

, find the value of

\dfrac{d^{2}y}{dx^{2}}

at the point

(2,2)

. (a)

1

(b)

-\dfrac{1}{2}

(c)

0

(d)

-\dfrac{3}{16}

Related theory

Higher-Order Derivatives
Advanced Differentiation
Implicit and parametric differentiation
Derivatives of implicit functions
Continuity and Differentiability

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