10. Let
Which of the following properties does f have on the interval (0,6)?
I. ln f exists.
II. f is continuous.
III. f is monotonic.
|
A. None |
B. I only |
C. II only |
|
D. III only |
E. The correct answer is not given by A, B, C, or D. |
Solution: The answer is C
Since the first function given in the definition factors we can write it as
Since the limit of f(x) is 4 from both the right and the left, the function is continuous at 4. Then, by inspection it is continuous on (0,6). It is not monotonic: Its initial value is 2, rises to 4, and then drops to -2 at x = 6. The negative values from x = 16/3 to x = 6 also keep it from having a log.