Question

Is `f(x)=-3x^5-2x^4-9x^2+x-7` concave or convex at `x=5`?

Answer 1

`f’’(5) = -8118` Less than zero, therefore concave.

Explanation:

`f’’(x) < 0` at `x = 5` (concave)
`f’’(x) > 0` at `x = 5` (convex)

`f’(x)=-15x^4-8x^3-18x+1`
`f’’(x)=-60x^3-24x^2-18`

`f’’(5)=-60(125)-24(25)-18 = -8118` Less than zero, therefore concave.