Algebra Examples

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

Step 1

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

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

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $5$ by $1$ .

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

Step 2.1.2

One to any power is one.

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

Step 2.1.3

Multiply $- 2$ by $1$ .

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

Step 2.2

Simplify by subtracting numbers.

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Step 2.2.1

Subtract $2$ from $5$ .

$f (1) = 3 - 2$

Step 2.2.2

Subtract $2$ from $3$ .

$f (1) = 1$

Step 2.3

The final answer is $1$ .

$1$

Step 3