Question

For what values of x is `f(x)=-x^3+x^2-x+5` concave or convex?

Answer 1

Second derivative is positive and hence it is convex or minimum.

Explanation:

`f’(x) = -3x^2 + 2x -1`

`f”(x) = -6x + 2 = 0`
`6x = 2 or x = 1/3`

Therefore it is convex or minimum.