Question

Is `f(x) =-x^3+(x-8)(x+3)` concave or convex at `x=1`?

Answer 1

concave

Explanation:

`f(x)=-x^3+x^2-5x-24`
`f'(x)=-3x^2+2x-5`
`f''(x)=-6x+2`

`f''(1)=-4`

Since `f''(1) <0`, the function is said to be concave down.