Find all open intervals on which the function f(x)=(x^2)/(x^2+4) is descreasing.?

Question

Precalc question!!! URGENT!!

Answer 1

Just differentiate it. You need f'(x) < 0.

By the quotient rule, f'(x) = (2x(x^2 + 4) - (x^2)(2x))/(x^2+4)^2.
Now, since the bottom is a square, thus positive, you just need the numerator to be < 0:
2x(x^2 + 4) - x^2 * 2x < 0
2x^3 + 8x - 2x^3 < 0
8x < 0
x < 0
Thus it is decreasing on (-∞,0).

Answer 2

for decreasing func f'(x)<0
f'(x)= 8x/(x^2+4)^2
f'(x)<0 for
x: (0 , -inf)
thanks