Question

COLLEGE MATH!!! Please help me!

Answer 1

(
`-\infty`, 0) and (8,
`\infty`)

Explanation:

Curve is concave downward when the second derivative is negative.

y' =
`(x^(2) )/(x^(2) -x+4)` , by the Fundamental Theorem of Calculus

y'' =
`(-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.