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

Jul 3, 2016

concave

#### Explanation:

$f \left(x\right) = - {x}^{3} + {x}^{2} - 5 x - 24$
$f ' \left(x\right) = - 3 {x}^{2} + 2 x - 5$
$f ' ' \left(x\right) = - 6 x + 2$

$f ' ' \left(1\right) = - 4$

Since $f ' ' \left(1\right) < 0$, the function is said to be concave down.