AP®MathsCollege BoardCalculus ABExam QuestionsUnit 5: Analytical Applications of DifferentiationBehaviors of Implicit Relations

Behaviors of Implicit Relations (College Board AP® Calculus AB)

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Behaviors of Implicit Relations

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Behaviors of Implicit Relations

1
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A curve goes through the point (4, 0). If the equation of the curve satisfies open parentheses x plus 3 y close parentheses fraction numerator d y over denominator d x end fraction equals 5 x minus 2 y, what is the value of fraction numerator d squared y over denominator d x squared end fraction at the point (4, 0)?

  • negative 85 over 4

  • 0

  • 5

  • 85 over 4

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2
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A curve has the equation 2 x squared minus 2 y squared minus 3 y equals 0. Find the number of critical points on this curve.

  • 0

  • 1

  • 2

  • 3

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3
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A curve has the equation x y plus x cubed plus y equals 0, where x not equal to negative 1.

Find the number of critical points on the curve.

  • 0

  • 1

  • 2

  • 3

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4
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A curve has the equation y equals x e to the power of y. What is the value of the second derivative of the curve at the origin?

  • 0

  • 1

  • 2

  • -2

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5
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Given that a curve has the equation sin space x space cos space y space equals fraction numerator space 1 over denominator 2 end fraction, what is an expression for fraction numerator d squared y over denominator d x squared end fraction?

  • cot space x space cot space y

  • negative csc squared x space cot space y space minus space csc squared y space cot space x

  • cot space y space open parentheses csc squared x space plus thin space cot squared x space csc squared y close parentheses

  • negative cot space y space open parentheses csc squared x space plus thin space cot squared x space csc squared y close parentheses

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