4. find the average rate of change of $f(x) = 4x^2 - 5x$ over the interval $-2, 0$
working:
answer: __________________

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $ f(x) $ over the interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. Here, $ a = -2 $ and $ b = 0 $, and $ f(x)=4x^{2}-5x $.

## Step2: Calculate $ f(-2) $
Substitute $ x = -2 $ into $ f(x) $:
$$
\begin{align*}
f(-2)&=4(-2)^{2}-5(-2)\
&=4\times4 + 10\
&=16 + 10\
&=26
\end{align*}
$$

## Step3: Calculate $ f(0) $
Substitute $ x = 0 $ into $ f(x) $:
$$
\begin{align*}
f(0)&=4(0)^{2}-5(0)\
&=0 - 0\
&=0
\end{align*}
$$

## Step4: Calculate the average rate of change
Using the formula $\frac{f(b)-f(a)}{b - a}$ with $ a=-2 $, $ b = 0 $, $ f(-2)=26 $ and $ f(0)=0 $:
$$
\begin{align*}
\text{Average rate of change}&=\frac{f(0)-f(-2)}{0-(-2)}\
&=\frac{0 - 26}{0 + 2}\
&=\frac{-26}{2}\
&=-13
\end{align*}
$$

# Answer:
$-13$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \( f(-2) \)

Step3: Calculate \( f(0) \)

Step4: Calculate the average rate of change

Answer: