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AP Calculus AB 2.2 Defining the Derivative of a Function and Using Derivative Notation Question Bank

Practise AP Calculus AB 2.2 questions by connecting derivative limits with tangent slopes and equations across representations.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • connect difference-quotient limits with derivative notation and instantaneous slope
  • write tangent-line equations from derivatives, tables, graphs and parametric motion

Covered syllabus points

CHA-2.B—Represent the derivative of a function as the limit of a difference quotient—Topic 2.2CHA-2.C—Determine the equation of a line tangent to a curve at a given point

2.2 Defining the Derivative of a Function and Using Derivative Notation question 1

[Maximum number: 1]

lim⁡h→0e2+h−e2h\lim _{h \rightarrow 0} \frac{e^{2+h}-e^{2}}{h} is

A

0

B

e2e^{2}

C

2e22 e^{2}

D

nonexistent

2.2 Defining the Derivative of a Function and Using Derivative Notation question 2

Table for Question 2.2 Defining the Derivative of a Function and Using Derivative Notation question 2 — AP Calculus AB

5. Let f be the function whose graph is shown above; the graph of f consists of

three line segments.

Let g be a differentiable function. The table above gives values of g and its

derivative g′g^{\prime} at various values of x.

Table for Question 2.2 Defining the Derivative of a Function and Using Derivative Notation question 2 — AP Calculus AB

(a) Let w be the function defined as w(x)=f(3 x)+g(x). Find an equation

of the tangent line to w at x=1.

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