Apentix/AP Calculus AB/Unit 5: Analytical Applications of Differentiation/Question

AP Calculus ABeasymcq1 pt

Let $f$ be differentiable on $[1,4]$ with $f(1)=2$ and $f(4)=8$ . Which statement is guaranteed by the Mean Value Theorem?

A.There is a number

c

in

(1,4)

with

f'(c)=2

.

B.There is a number

c

in

(1,4)

with

f'(c)=6

.

C.There is a number

c

in

(1,4)

with

f(c)=2

.

D.There is a number

c

in

(1,4)

with

f'(c)=10

.

Explanation

Core Concept

The MVT guarantees a number $c$ in $(1,4)$ with $f'(c)$ equal to the average rate of change. Here $(f(4)-f(1))/(4-1)=(8-2)/3=2$ .

Correct Answer

AThere is a number $c$ in $(1,4)$ with $f'(c)=2$ .

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