Find the Maximum/Minimum Value f(x)=-0.4x^2+2.1x+6

$f (x) = - 0.4 x^{2} + 2.1 x + 6$

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 $b$ .

$x = - \frac{2.1}{2 (- 0.4)}$

Remove parentheses.

$x = - \frac{2.1}{2 (- 0.4)}$

Simplify $- \frac{2.1}{2 (- 0.4)}$ .

Multiply $2$ by $- 0.4$ .

$x = - \frac{2.1}{- 0.8}$

Divide $2.1$ by $- 0.8$ .

$x = - - 2.625$

Multiply $- 1$ by $- 2.625$ .

$x = 2.625$

Step 3

Evaluate $f (2.625)$ .

Replace the variable $x$ with $2.625$ in the expression.

$f (2.625) = - 0.4 {(2.625)}^{2} + 2.1 (2.625) + 6$

Simplify the result.

Simplify each term.

Raise $2.625$ to the power of $2$ .

$f (2.625) = - 0.4 \cdot 6.890625 + 2.1 (2.625) + 6$

Multiply $- 0.4$ by $6.890625$ .

$f (2.625) = - 2.75625 + 2.1 (2.625) + 6$

Multiply $2.1$ by $2.625$ .

$f (2.625) = - 2.75625 + 5.5125 + 6$

Simplify by adding numbers.

Add $- 2.75625$ and $5.5125$ .

$f (2.625) = 2.75625 + 6$

Add $2.75625$ and $6$ .

$f (2.625) = 8.75625$

The final answer is $8.75625$ .

$8.75625$

Step 4

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

$(2.625, 8.75625)$

Step 5

Find the Maximum/Minimum Value f(x)=-0.4x^2+2.1x+6

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