Question

For what values of x is `f(x)=(x-1)(x-6)(x-2)` concave or convex?

Answer 1

See below.

Explanation:

`f(x) = (x-1)(x6)(x-2) = x^3-9x^2+20x-12`

`f'(x) = 3x^2-18x+20`

`f''(x) = 6x-18`

`f''(x)` is negative for `x < 3`, so `f` is concave (or concave down) on `(-oo,3)`.

`f''(x)` is positive for `3 < x`, so `f` is convex (or concave up) on `(3,oo)`.