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AP® Calculus AB-BC

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Moderate

Limit of a Quotient and Its Original Function

APCALC-9YSFVG

Let $f(x)$ be a function such that $\lim \limits_{x \to 10} \frac{f(x)-f(10)}{x-10} =-1$. Which of the following statements must be TRUE?

A

$\lim \limits_{x \to 10} f(x)$ does not exist

B

$f(10)=-1$

C

$f’(10)=-1$

D

$f(x)$ is continuous at $x=-1$