A point moves along the ellipse

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

Problem

4x^{2}+9y^{2}=36

. At the instant the point is at

(\sqrt{2},\,2)

, the

x

–coordinate is decreasing. Determine whether

\dfrac{dy}{dt}

is positive, negative, or zero at that instant and state a brief reason for your answer.

Related theory

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

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