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AP Calculus BC 5.12: Critical Points of Implicit Relations

Practise AP Calculus BC 5.12 by differentiating implicit relations, locating vertical tangents, and combining derivative conditions with the original equation.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • Use implicit differentiation to set 2y − x = 0, then solve alongside x³ + xy − y² = 10 for the vertical tangent.

FUN-4.D—Determine critical points of implicit relations question 1

[Maximum number: 1]

The curve defined by x3+xy−y2=10x^{3}+x y-y^{2}=10 has a vertical tangent line when x=

A

1.037

B

1.087

C

2.074

D

2.096

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