Find intervals of increase or decrease

Question

F(x)=(5x)/(x^2 + 1)

not supposed to use graphing calculator make use of number line I just don’t know how to start it

Answer 1

F(x) = (5x) / (x² + 1)

F'(x) = [5(x²+1) - 10x²] / (x²+1)²

F'(x) = 0 when -5x² + 5 = 0 So, x² = 1. x = 1 or -1

When x < -1, F'(x) < 0 So, F(x) is decreasing

When -1<x<1, F'(x) > 0 . So, F(x) is increasing

When x > 1, F'(x) < 0 So, F(x) is decreasing

Answer 2

The function is odd: f(-x) = -f(x).

It is symmetric through the origin.

f(0) = 0

For 0 < x < 1 the graph rises to 2.5 then decreases