Question

COLLEGE MATH!!! Please help me!

Answer 1

Answer:

( $-\infty$, 0) and (8, $\infty$)  

Step-by-step explanation:

Curve is concave downward when the second derivative is negative.

y' = $\frac{x^{2} }{x^{2} -x+4}$ , by the Fundamental Theorem of Calculus

y'' =   $\frac{-x^2+8x}{\left(x^2-x+4\right)^2}$ , which has a denominator that is always positive. The numerator $-x^2+8x$ 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.