Question

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

Answer 1

The function is concave.

Explanation:

Calculate the first and second derivatives

`f(x)=5x^5-x^2+4x+3`

`f'(x)=25x^4-2x+4`

`f''(x)=100x^3-2`

When `x=-4`,

`f''(-4)=100*(-4)^3-2`

`=-6402`

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