Finding the range of ln(-x² + x + 6)

[fiziksfun]

Let f(x)= ln(-x^2+x+6)

Find the range of f(x). Use f'(x) to support your answer.

Attempt at a solution:

Find the max. value of the range is easy. I found the derivative and set it equal to zero. My REAL PROBLEM is finding the minimum value of the range.

The function's domain must be between -2 and 3 becus you cannot take the natural lg of a negative number or zero.
SO, as f(x) approaches, 3 or -2, does it approach negative infinity??
Am I right when I say its lower range is negative infinity?? HELP!

 

[Dick]

As x approaches -2 from above or 3 from below, then -x^2+x+6 approaches 0 from above. So yes, you are right.