Find the Maximum/Minimum Value f(x)=-0.1x^2+0.6x+7

$f (x) = - 0.1 x^{2} + 0.6 x + 7$

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 $b$ .

$x = - \frac{0.6}{2 (- 0.1)}$

Remove parentheses.

$x = - \frac{0.6}{2 (- 0.1)}$

Simplify $- \frac{0.6}{2 (- 0.1)}$ .

Multiply $2$ by $- 0.1$ .

$x = - \frac{0.6}{- 0.2}$

Divide $0.6$ by $- 0.2$ .

$x = - - 3$

Multiply $- 1$ by $- 3$ .

$x = 3$

Step 3

Evaluate $f (3)$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = - 0.1 {(3)}^{2} + 0.6 (3) + 7$

Simplify the result.

Simplify each term.

Raise $3$ to the power of $2$ .

$f (3) = - 0.1 \cdot 9 + 0.6 (3) + 7$

Multiply $- 0.1$ by $9$ .

$f (3) = - 0.9 + 0.6 (3) + 7$

Multiply $0.6$ by $3$ .

$f (3) = - 0.9 + 1.8 + 7$

Simplify by adding numbers.

Add $- 0.9$ and $1.8$ .

$f (3) = 0.9 + 7$

Add $0.9$ and $7$ .

$f (3) = 7.9$

The final answer is $7.9$ .

$7.9$

Step 4

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

$(3, 7.9)$

Step 5

Find the Maximum/Minimum Value f(x)=-0.1x^2+0.6x+7

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