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AP Calculus AB Fun 4 E Justify Conclusions About the Behavior of an Implicitly Defined Function Based on Evidence From Its Derivatives Questions

Practise implicit-differentiation questions by finding derivatives from equations and reasoning about the behavior of implicitly defined functions.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • differentiate an implicitly defined equation with respect to x
  • use derivative evidence to justify behavior of an implicitly defined function

AP Calculus AB Fun 4 E Justify Conclusions About the Behavior of an Implicitly Defined Function Based on Evidence From Its Derivatives Questions question 1

Given the following differential equation tart fraction numerator d y over denominator d x end fraction equals x minus 2 y plus 1

Find the second derivative, et fraction numerator d squared y over denominator d x squared end fraction , 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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