Exam version: 77
9. Let a be a constant and let $f(x)$ be a function with domain $(-\infty, \infty)$. Assume that $f$ satisfies
$\lim_{x \to 2^-} \frac{f(x) - f(2)}{x - 2} = 4 + a$, and $\lim_{x \to 2^+} \frac{f(x) - f(2)}{x - 2} = 9$.
Which of the following statements is TRUE?
(a) $f'(2) = \frac{a + 4}{9}$
(b) If $a = 5$, then $f'(x) = 9$ for all values of $x$.
(c) $f'(2)$ does not exist for all values of $a$.
(d) If $a \neq 5$, then $f$ is not continuous at $x = 2$.
(e) If $a = 5$, then $f'(2) = 9$.
10. Consider the function
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