Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question

AP Calculus ABhardmcq1 pt

Suppose $f$ is continuous on $[0,3]$ with $f(0)=-4$ and $f(3)=1$ . Which statement is guaranteed by the Intermediate Value Theorem?

A.There is a

c

in

(0,3)

with

f(c)=2

.

B.There is a

c

in

(0,3)

with

f(c)=0

.

C.

f

is differentiable on

(0,3)

.

D.

f(c)=0

for every

c

in

(0,3)

.

Explanation

Core Concept

Since $f$ is continuous and $f(0)=-4<0<1=f(3)$ , the IVT guarantees some $c$ in $(0,3)$ where $f(c)=0$ .

Correct Answer

BThere is a $c$ in $(0,3)$ with $f(c)=0$ .

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