Question

Is `f(x) =(x-2)^3/(x^2-7)` concave or convex at `x=2`?

Answer 1

`f''(2)=-2/3`

Explanation:

We get
`f'(x)=2(x-2)(2x-7))/(x^2-7)^2`

`f'''(x)=-(2*(4x^3-33x^2+84x-77))/(x^2-7)`

`f''(2)=-2/3<0`
The function is concave for `x=2`