Is f(x) =(x-1)^3/(x^2-4) concave or convex at x=3?

1 Answer
Sep 24, 2017

concave up

Explanation:

f'(x) = (3(x-1)^2)/(2x)
f''(x) = (6(x-1))/2

Substitute in x=3
f''(3)=(6(3-1))/2
=6

When double derivatives are positive, they concave up (smiley face = positive).