ven $$ f(x)=-x^{2}+12 x-39 $$ what is e average rate of change of $$ f(x) $$ from to $$ f(5) $$ to $$ f(7 $$ the average rate of change is $$ \frac{-3}{4} $$, enter it as $$ -3 / 4 $$ with no paces.

Question

UpStudy AI · Accepted Answer

To find the average rate of change of the function $$ f(x) = -x^{2} + 12x - 39 $$ from $$ f(5) $$ to $$ f(7) $$, we will follow these steps:

1. Calculate $$ f(5) $$.
2. Calculate $$ f(7) $$.
3. Use the formula for the average rate of change, which is given by:

$$
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
$$

where $$ a = 5 $$ and $$ b = 7 $$.

Let's start by calculating $$ f(5) $$ and $$ f(7) $$.

First, we will calculate $$ f(5) $$:

$$
f(5) = -5^{2} + 12 \cdot 5 - 39
$$

Next, we will calculate $$ f(7) $$:

$$
f(7) = -7^{2} + 12 \cdot 7 - 39
$$

Now, let's compute these values.
Calculate the value by following steps:
- step0: Calculate:
  $$-5^{2}+12\times 5-39$$
- step1: Multiply the numbers:
  $$-5^{2}+60-39$$
- step2: Evaluate the power:
  $$-25+60-39$$
- step3: Calculate:
  $$-4$$
Calculate or simplify the expression $$ -7^2 + 12*7 - 39 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-7^{2}+12\times 7-39$$
- step1: Multiply the numbers:
  $$-7^{2}+84-39$$
- step2: Evaluate the power:
  $$-49+84-39$$
- step3: Calculate:
  $$-4$$
We have calculated the following:

- $$ f(5) = -4 $$
- $$ f(7) = -4 $$

Now, we can find the average rate of change using the formula:

$$
\text{Average Rate of Change} = \frac{f(7) - f(5)}{7 - 5} = \frac{-4 - (-4)}{7 - 5} = \frac{0}{2} = 0
$$

Thus, the average rate of change of $$ f(x) $$ from $$ f(5) $$ to $$ f(7) $$ is $$ 0 $$.

If you need to enter the average rate of change as a fraction, it would be $$ 0/1 $$.
The average rate of change of $$ f(x) $$ from $$ f(5) $$ to $$ f(7) $$ is $$ 0 $$.

ven what is
e average rate of change of from to to
the average rate of change is , enter it as with no
paces.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions

ven what is e average rate of change of from to to the average rate of change is , enter it as with no paces.