AP Calculus ABeasymcq1 pt

For which function does Rolle's Theorem guarantee a number $c$ in $(-2,2)$ with $f'(c)=0$ ?

f(x)=x^3

f(x)=x^2

f(x)=e^x

f(x)=\dfrac{1}{x}

Explanation

Core Concept

$f(x)=x^2$ is continuous on $[-2,2]$ and differentiable on $(-2,2)$ , and $f(-2)=f(2)=4$ . Rolle's Theorem therefore guarantees some $c$ in $(-2,2)$ with $f'(c)=0$ .

Correct Answer

B $f(x)=x^2$

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Practice Unit 5: Analytical Applications of Differentiation Questions →

For which function does Rolle's Theorem guarantee a number ccc in (−2,2)(-2,2)(−2,2) with f′(c)=0f'(c)=0f′(c)=0?

Explanation

Core Concept

Correct Answer

More Unit 5: Analytical Applications of Differentiation practice questions

For which function does Rolle's Theorem guarantee a number $c$ in $(-2,2)$ with $f'(c)=0$ ?