AP®︎ Calculus BC: Topic 4.6 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 4.6 of AP Calculus BC – Approximating Values of a Function Using Local Linearity and Linearization.

Questions List

Topic 4.6

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Question 1 Easy

Figure

The function ff is differentiable. The three windows show successive zooms of its graph around the same point P=(a,f(a))P=(a,f(a)).

Which statement is true?

ANear PP, the graph looks more and more like a horizontal line, so the constant value f(a)f(a) gives the local linear approximation.
BNear PP, the graph becomes exactly its tangent line, so the tangent line equals ff throughout some interval around aa.
CNear PP, the graph looks more and more like its tangent line, so the tangent line approximates ff well for xx close to aa.
DNear PP, the graph looks more and more like its tangent line, so the tangent line approximates ff equally well for all xx.

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus BC Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.

Topic 4.6: Approximating Values of a Function Using Local Linearity and Linearization

Learning Objective: CHA-3.F

Approximate a value on a curve using the equation of a tangent line.

Essential Knowledge: CHA-3.F.1

The tangent line is the graph of a locally linear approximation of the function near the point of tangency.

Essential Knowledge: CHA-3.F.2

For a tangent line approximation, the function’s behavior near the point of tangency may determine whether a tangent line value is an underestimate or an overestimate of the corresponding function value.

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