Find the open intervals on which f is increasing and decreasing.

Question

Let f(x)=(x-6)/(x+6). Find the open intervals on which f is increasing and decreasing. Then determine the x-coordinates of all relative maxima and minima.

 

1. f is increasing on the intervals:_______

2. f is decreasing on the intervals:_______

3. The relative maxima of f occur at x=_______

4. The relative minima of f occur at x=_______

Answer 1

f(x) = (x-6)/(x+6)

 

f'(x) = [(x+6)(1) - (x-6)(1)]/(x+6)² = 12/(x+6)²

 

f'(x) > 0 for all x ≠ -6

 

f is increasing on (-∞, -6) ∪ (-6, ∞)

 

f is never decreasing

 

There are no relative extrema.