Answer:
( [tex]-\infty[/tex], 0) and (8, [tex]\infty[/tex])
Step-by-step explanation:
Curve is concave downward when the second derivative is negative.
y' = [tex]\frac{x^{2} }{x^{2} -x+4}[/tex] , by the Fundamental Theorem of Calculus
y'' = [tex]\frac{-x^2+8x}{\left(x^2-x+4\right)^2}[/tex] , which has a denominator that is always positive. The numerator [tex]-x^2+8x[/tex] is negative when x > 0 and when x < 8. So that is when y'' is negative, and consequently when the curve y is concave down.
