Find the Maximum/Minimum Value -1/7x^2+100x

$- \frac{1}{7} x^{2} + 100 x$

Step 1

Combine $x^{2}$ and $\frac{1}{7}$ .

$f (x) = - \frac{x^{2}}{7} + 100 x$

Step 2

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 3

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

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

$x = - \frac{100}{2 (- 0.\overline{142857})}$

Remove parentheses.

$x = - \frac{100}{2 (- 0.\overline{142857})}$

Simplify $- \frac{100}{2 (- 0.\overline{142857})}$ .

Cancel the common factor of $100$ and $2$ .

Factor $2$ out of $100$ .

$x = - \frac{2 \cdot 50}{2 \cdot - 0.\overline{142857}}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 0.\overline{142857}$ .

$x = - \frac{2 \cdot 50}{2 (- 0.\overline{142857})}$

Cancel the common factor.

$x = - \frac{2 \cdot 50}{2 \cdot - 0.\overline{142857}}$

Rewrite the expression.

$x = - \frac{50}{- 0.\overline{142857}}$

Simplify the expression.

Divide $50$ by $- 0.\overline{142857}$ .

$x = - - 350$

Multiply $- 1$ by $- 350$ .

$x = 350$

Step 4

Evaluate $f (350)$ .

Replace the variable $x$ with $350$ in the expression.

$f (350) = - \frac{{(350)}^{2}}{7} + 100 (350)$

Simplify the result.

Simplify each term.

Raise $350$ to the power of $2$ .

$f (350) = - \frac{122500}{7} + 100 (350)$

Divide $122500$ by $7$ .

$f (350) = - 1 \cdot 17500 + 100 (350)$

Multiply $- 1$ by $17500$ .

$f (350) = - 17500 + 100 (350)$

Multiply $100$ by $350$ .

$f (350) = - 17500 + 34999.99999999$

Add $- 17500$ and $34999.99999999$ .

$f (350) = 17499.99999999$

The final answer is $17499.99999999$ .

$17499.99999999$

Step 5

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

$(350, 17499.99999999)$

Step 6

Find the Maximum/Minimum Value -1/7x^2+100x

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