Determine the open intervals on which the graph is concave upward or concave downward. f(x) = 28/(x^2 + 3)

Question

 Determine the open intervals on which the graph is concave upward or concave downward. f(x) = 28/(x^2 + 3)

Answer 1

f'(x) = -56x/(x² +3)²

f"(x) = 168(x² -1)/(x² +3)²

f"(x) < 0 for |x| < 1 ⇒ f is concave downward for x ∈ (-1, 1)

f"(x) > 0 for |x| > 1 ⇒ f is concave upward for x ∈ (-∞,-1) or x ∈ (1, ∞)