A continuous function $f$, defined for all $x$, has the following properties:

1. $f$ is decreasing
2. $f$ is concave up
3. $f(9) = -2$
4. $f'(9) = -\frac{1}{4}$

Sketch a possible graph for $f$, and use it to answer the following questions about $f$.

A. For each of the following intervals, what is the minimum and maximum number of zeros $f$ could have in the interval? (Note that if there must be exactly N zeros in an interval, the minimum and maximum are both N.)

 minimum maximum $-\infty < x \le 0$ $0 < x \le 1$ $1 < x < 9$ $9 \le x < \infty$

B. Are any of the following possible values for $f'(1)$? (Enter your answer as a comma-separated list, or enter 'none' if none of them are possible.) $-3$, $-2$, $-1$, $-\frac{1}{5}$, $0$, $\frac{1}{5}$, $1$, $2$, $3$.
possible values: $f'(1) =$

C. What happens to $f$ as $x\to-\infty$?
$\lim\limits_{x\to-\infty} f(x) =$
(Enter the value, 'infinity' or '-infinity' for $\infty$ or $-\infty$, or 'none' if there is no limit.)

You can earn partial credit on this problem.