Consider the curve

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

Problem

Consider the curve

x^{2}-xy+y=4

. Determine every value of

x

at which the curve has a horizontal tangent. For each such

x

–value, decide whether the corresponding point on the curve is a local extremum of

y

with respect to

x

or a point of inflection.

Related theory

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

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