Question

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

Answer 1

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).