Finite Math Examples

$C (x) = 0.001 x^{2} - 0.15 x + 18.5$

Step 1

The minimum of a quadratic function occurs at $x = - \frac{b}{2 a}$ . If $a$ is positive, the minimum value of the function is $f (- \frac{b}{2 a})$ .

$f_{min}$ $x = a x^{2} + b x + c$ occurs at $x = - \frac{b}{2 a}$

Step 2

Find the value of $x = - \frac{b}{2 a}$ .

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Step 2.1

Substitute in the values of $a$ and $b$ .

$x = - \frac{- 0.15}{2 (0.001)}$

Step 2.2

Remove parentheses.

$x = - \frac{- 0.15}{2 (0.001)}$

Step 2.3

Simplify $- \frac{- 0.15}{2 (0.001)}$ .

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Step 2.3.1

Multiply $2$ by $0.001$ .

$x = - \frac{- 0.15}{0.002}$

Step 2.3.2

Divide $- 0.15$ by $0.002$ .

$x = - - 75$

Step 2.3.3

Multiply $- 1$ by $- 75$ .

$x = 75$

Step 3

Evaluate $f (75)$ .

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Step 3.1

Replace the variable $x$ with $75$ in the expression.

$C (75) = 0.001 {(75)}^{2} - 0.15 \cdot 75 + 18.5$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Raise $75$ to the power of $2$ .

$C (75) = 0.001 \cdot 5625 - 0.15 \cdot 75 + 18.5$

Step 3.2.1.2

Multiply $0.001$ by $5625$ .

$C (75) = 5.625 - 0.15 \cdot 75 + 18.5$

Step 3.2.1.3

Multiply $- 0.15$ by $75$ .

$C (75) = 5.625 - 11.25 + 18.5$

Step 3.2.2

Simplify by adding and subtracting.

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Step 3.2.2.1

Subtract $11.25$ from $5.625$ .

$C (75) = - 5.625 + 18.5$

Step 3.2.2.2

Add $- 5.625$ and $18.5$ .

$C (75) = 12.875$

Step 3.2.3

The final answer is $12.875$ .

$12.875$

Step 4

Use the $x$ and $y$ values to find where the minimum occurs.

$(75, 12.875)$

Step 5