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

AP Calculus ABhardmcq1 pt

Let $f(x)=x^3-x-1$ . Given that $f(1)=-1$ and $f(2)=5$ , which interval is guaranteed to contain a zero of $f$ by the Intermediate Value Theorem?

A.

(1,2)

B.

(0,1)

C.

(-1,0)

D.

(2,3)

Explanation

Core Concept

$f$ is a polynomial, hence continuous everywhere. Since $f(1)=-1<0$ and $f(2)=5>0$ , the IVT guarantees a $c$ in $(1,2)$ with $f(c)=0$ .

Correct Answer

A $(1,2)$

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