Find the Maximum/Minimum Value f(x)=-0.1x^2+0.7x+8

$f (x) = - 0.1 x^{2} + 0.7 x + 8$

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 $b$ .

$x = - \frac{0.7}{2 (- 0.1)}$

Remove parentheses.

$x = - \frac{0.7}{2 (- 0.1)}$

Simplify $- \frac{0.7}{2 (- 0.1)}$ .

Multiply $2$ by $- 0.1$ .

$x = - \frac{0.7}{- 0.2}$

Divide $0.7$ by $- 0.2$ .

$x = - - 3.5$

Multiply $- 1$ by $- 3.5$ .

$x = 3.5$

Step 3

Evaluate $f (3.5)$ .

Replace the variable $x$ with $3.5$ in the expression.

$f (3.5) = - 0.1 {(3.5)}^{2} + 0.7 (3.5) + 8$

Simplify the result.

Simplify each term.

Raise $3.5$ to the power of $2$ .

$f (3.5) = - 0.1 \cdot 12.25 + 0.7 (3.5) + 8$

Multiply $- 0.1$ by $12.25$ .

$f (3.5) = - 1.225 + 0.7 (3.5) + 8$

Multiply $0.7$ by $3.5$ .

$f (3.5) = - 1.225 + 2.45 + 8$

Simplify by adding numbers.

Add $- 1.225$ and $2.45$ .

$f (3.5) = 1.225 + 8$

Add $1.225$ and $8$ .

$f (3.5) = 9.225$

The final answer is $9.225$ .

$9.225$

Step 4

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

$(3.5, 9.225)$

Step 5

Find the Maximum/Minimum Value f(x)=-0.1x^2+0.7x+8

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