So I have to figure out the intervals of increase and decrease for 1/x^2+2. For some reason i keep on getting the function as increasing throughout. My derivativewas-2x(x^2+2)^-2. Someone help

Answer 1

y = 1/(x^2+2)
y' = -2x/(x^2+2)^2

Since the denominator is always positive,
y' > 0 when x < 0
y' < 0 when x > 0

So, y is increasing for all x < 0 and decreasing for all x > 0
This makes sense, since y is just a bell curve, with a maximum at x=0