Question

Is `f(x)=-x^5-2x^2-6x+3` concave or convex at `x=-4`?

Answer 1

The function is convex

Explanation:

Calculate the first and second derivatives

`f(x)=-x^5-2x^2-6x+3`

`f'(x)=-5x^4-4x-6`

`f''(x)=-20x^3-4`

Therefore, when `x=-4`

`f''(-4)=-20*(-4)^3-4=1280-4=1276`

As `f''(x)>0`, the function is convex at `x=-4`