Question

Inteval over which y=1/x^2 decreasing

Answer 1

Answer:

Correct option is

B

(1,∞)

C

(−∞,−1)

y=x/(1+x2)

y′=(1+x2)2(1+x2)−2x⋅x=(1+x2)21−x2

Since (1+x2)2>0 for all x

Therefore y′<0 for 1−x2<0

⇒ x>1 or x<−1

Therefore, x∈(−∞,−1) or x∈(1,∞).

Thus x/(1+x2) decreases in  (−∞,−1] or [1,∞).