AP®︎ Calculus AB: Topic 3.6 Practice Test

Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 3.6 of AP Calculus AB – Calculating Higher-Order Derivatives.


Questions List

Topic 3.6

Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q11
Q12
Q13
Q14
Q15
Q16
Q17
Q18
Q19
Q20
Q21

Question 1 Easy

If f′(x)=x3−4xf'(x) = x^3 - 4x, then f′′(x)=f''(x) =

Ax44−2x2\frac{x^4}{4} - 2x^2
B6x6x
C3x2−43x^2 - 4
D3x23x^2

What You’re Being Tested On:

Explore the learning objectives taken directly from the College Board’s AP® Calculus AB 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 3.6: Calculating Higher-Order Derivatives

Learning Objective: FUN-3.F

Determine higher order derivatives of a function.

Essential Knowledge: FUN-3.F.1

Differentiating f' produces the second derivative f'', provided the derivative of f' exists; repeating this process produces higher-order derivatives of f.

Essential Knowledge: FUN-3.F.2

Higher-order derivatives are represented with a variety of notations. For y = f(x), notations for the second derivative include d^2y/dx^2, f''(x), and y''. Higher-order derivatives can be denoted d^n y/dx^n or f^(n)(x).