Find the Maximum/Minimum Value -0.001x^2+3x-1800

$- 0.001 x^{2} + 3 x - 1800$

Step 1

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

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

Step 2

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

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

$x = - \frac{3}{2 (- 0.001)}$

Remove parentheses.

$x = - \frac{3}{2 (- 0.001)}$

Simplify $- \frac{3}{2 (- 0.001)}$ .

Multiply $2$ by $- 0.001$ .

$x = - \frac{3}{- 0.002}$

Divide $3$ by $- 0.002$ .

$x = - - 1500$

Multiply $- 1$ by $- 1500$ .

$x = 1500$

Step 3

Evaluate $f (1500)$ .

Replace the variable $x$ with $1500$ in the expression.

$f (1500) = - 0.001 {(1500)}^{2} + 3 (1500) - 1800$

Simplify the result.

Simplify each term.

Raise $1500$ to the power of $2$ .

$f (1500) = - 0.001 \cdot 2250000 + 3 (1500) - 1800$

Multiply $- 0.001$ by $2250000$ .

$f (1500) = - 2250 + 3 (1500) - 1800$

Multiply $3$ by $1500$ .

$f (1500) = - 2250 + 4500 - 1800$

Simplify by adding and subtracting.

Add $- 2250$ and $4500$ .

$f (1500) = 2250 - 1800$

Subtract $1800$ from $2250$ .

$f (1500) = 450$

The final answer is $450$ .

$450$

Step 4

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

$(1500, 450)$

Step 5

Find the Maximum/Minimum Value -0.001x^2+3x-1800

Related Questions

Support LCMGCF.com by disabling your adblocker.