Question

The curve y= (1-x)/(x-3) is concave up when:

Answer 1

concavity is determined by 2nd derivative
concave up when f''(x) > 0
concave down when f''(x) < 0

use quotient rule to find y'
y' = [ -(x-3)-(1-x)] /(x-3)^2 = 2/(x-3)^2

y'' = -4/(x-3)^3

--> -4/(x-3)^3 > 0

--> (x-3)^3 < 0

--> x-3 < 0

--> x < 3