Algebra Examples

$f (x) = x^{3} - 6 x^{2} + 1$ is concave down at $x = 1$

Step 1

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

$f (1) = {(1)}^{3} - 6 {(1)}^{2} + 1$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

One to any power is one.

$f (1) = 1 - 6 {(1)}^{2} + 1$

Step 2.1.2

One to any power is one.

$f (1) = 1 - 6 \cdot 1 + 1$

Step 2.1.3

Multiply $- 6$ by $1$ .

$f (1) = 1 - 6 + 1$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Subtract $6$ from $1$ .

$f (1) = - 5 + 1$

Step 2.2.2

Add $- 5$ and $1$ .

$f (1) = - 4$

Step 2.3

The final answer is $- 4$ .

$- 4$

Step 3