Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question

AP Calculus ABeasymcq1 pt

The average rate of change of a function $f$ on the interval $[a,b]$ equals the slope of which of the following lines?

A.The line tangent to the graph of

f

at

x=a

B.The secant line through

(a,f(a))

and

(b,f(b))

C.The line tangent to the graph of

f

at

x=b

D.The horizontal line

y=f(a)

Explanation

Core Concept

The average rate of change is $\dfrac{f(b)-f(a)}{b-a}$ , which is exactly the slope of the secant line through the two endpoints. A secant line connects two points on the curve.

Correct Answer

BThe secant line through $(a,f(a))$ and $(b,f(b))$

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