AnswersAP Calculus AB - MA5186 ADerivatives of FunctionsQuestion 2
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Derivatives of Functions

Question 2 • AP Calculus AB - MA5186 A

Which statements are true regarding the rates of change of a function? Check all that apply. The slope of the tangent line is the instantaneous rate of change of a function.The slope of the tangent line is the average rate of change of a function between two points. The slope of the secant line is the instantaneous rate of change of a function. The slope of the secant line is the average rate of change of a function between two points. The slope of the tangent line can be found by taking the limit of the difference quotient.

Answer
A
The slope of the tangent line is the instantaneous rate of change of a function.
B
The slope of the tangent line is the average rate of change of a function between two points.
C
The slope of the secant line is the instantaneous rate of change of a function.
D
The slope of the secant line is the average rate of change of a function between two points.
E
The slope of the tangent line can be found by taking the limit of the difference quotient.

Explanation

The slope of a tangent line at a point gives the function’s instantaneous rate of change, so A is true. A secant line passes through two points on the function, and its slope gives the average rate of change between them, so D is true. Taking the limit of the difference quotient as the interval shrinks to zero gives the tangent slope, making E true. The other statements reverse the roles of tangent and secant slopes.

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