Question

Find the intervals on which f(x) is increasing and decreasing using the, given, first derivative.
f'(x)=(-2x)/(x^2-4)^2

Answer 1

\[f'(x)=\frac{ -2x }{ (x^2-4)^2}\]

Answer 2

evidently the denominator is always positive (unless it is zero, where the function is undefined)
so the only question is, for which \(x\) is \(-2x>0\) and that would be if \(x<0\)

Answer 3

oh, that answer was for "increasing" so increasing if \(x<0\) decreasing if \(x>0\) and obviously undefined at \(x=2, x=-2\)