AP Calculus BC 5.12 Exploring Behaviors of Implicit Relations Questions

Use first and second implicit derivatives to locate critical points or vertical tangents and justify increasing, decreasing or concavity behavior.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

FUN-4.D—Determine critical points of implicit relations FUN-4.E—Justify conclusions about the behavior of an implicitly defined function based on evidence from its derivatives

[Maximum number: 1]

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

1.037

1.087

2.074

2.096

Given the following differential equation .

Find the second derivative, $\frac{d^{2} y}{d x^{2}}$ , in terms of x and y. The region in the x y-plane where all the solution curves to the differential equation are concave down can be expressed as a linear inequality.

Find this region.

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Covered syllabus points

Question 1

Question 2