Evaluate the Function f(x)=5x-2x^3-2 is concave down at x=1

$f (x) = 5 x - 2 x^{3} - 2$ is concave down at $x = 1$

Replace the variable $x$ with $1$ in the expression.

$f (1) = 5 (1) - 2 {(1)}^{3} - 2$

Simplify the result.

Simplify each term.

Multiply $5$ by $1$ .

$f (1) = 5 - 2 {(1)}^{3} - 2$

One to any power is one.

$f (1) = 5 - 2 \cdot 1 - 2$

Multiply $- 2$ by $1$ .

$f (1) = 5 - 2 - 2$

Simplify by subtracting numbers.

Subtract $2$ from $5$ .

$f (1) = 3 - 2$

Subtract $2$ from $3$ .

$f (1) = 1$

The final answer is $1$ .

$1$