Chapter 3: Q. 7 (page 175)

Determine whether $f (x) = - 2 x^{2} + 12 x + 3$ has a maximum or minimum value. Then find the maximum or minimum value.

Short Answer

Expert verified

The quadratic function has a maximum value. The maximum value is $21$ .

Step by step solution

Step 1. Given information.

Determine whether $f (x) = - 2 x^{2} + 12 x + 3$ has a maximum or minimum value. Then find the maximum or minimum value.

Step 2. Compare the function.

Compare

$f (x) = - 2 x^{2} + 12 x + 3 to f (x) = a x^{2} + b x + c Then a = - 2, b = 12 and c = 3$

Since $a < 0$ the graph of f opens down, so the vertex is a maximum value occurs at

$x = - \frac{b}{2 a} = - \frac{12}{2 (- 2)} = \frac{12}{4} = 3$

The maximum value is

$f (- \frac{b}{2 a}) = f (3) = - 2 {(3)}^{2} + 12 (3) + 3 = - 18 + 36 + 3 = 21$

Step 3. Conclusion.

The quadratic function has a maximum value. The maximum value is $21$ .

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Determine whether $f (x) = - 2 x^{2} + 12 x + 3$ has a maximum or minimum value. Then find the maximum or minimum value.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare the function.

Step 3. Conclusion.

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Determine whether f(x)=-2x2+12x+3has a maximum or minimum value. Then find the maximum or minimum value.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare the function.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Determine whether $f (x) = - 2 x^{2} + 12 x + 3$ has a maximum or minimum value. Then find the maximum or minimum value.