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

AP Calculus ABhardmcq1 pt

Let $f$ be a function for which $\lim_{h \to 0} \frac{f(3+h) - f(3)}{h} = -4$ . Which of the following must be true?

A.The instantaneous rate of change of

f

at

x=3

is

-4

.

B.The average rate of change of

f

between

x=3

and

x=4

is

-4

.

C.The slope of the secant line through

(3, f(3))

and

(3+h, f(3+h))

is always

-4

for any value of

h

.

D.The function value

f(3)

is equal to

-4

.

Explanation

Core Concept

The given limit is the definition of the derivative of $f$ at $x=3$ , which conceptually represents the instantaneous rate of change of the function at that exact point.

Correct Answer

AThe instantaneous rate of change of $f$ at $x=3$ is $-4$ .

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