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4.1 - 4.2 - quiz
score: 0/7 answered: 0/7
question 1
find the average rate of change of the function $f(x) = 2x^2 - 5x + 4$, on the interval $x \in -1, 0$.
average rate of change =
give exact answer!

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for average rate of change
The average rate of change of a function $ f(x) $ on the interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. Here, $ a=-1 $, $ b = 0 $, and $ f(x)=2x^{2}-5x + 4 $.

## Step2: Calculate $ f(-1) $
Substitute $ x=-1 $ into $ f(x) $:
$$
\begin{align*}
f(-1)&=2(-1)^{2}-5(-1)+4\
&=2(1)+5 + 4\
&=2 + 5+4\
&=11
\end{align*}
$$

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

## Step4: Apply the average rate of change formula
Using $ a=-1 $, $ b = 0 $, $ f(-1)=11 $, and $ f(0)=4 $:
$$
\begin{align*}
\text{Average rate of change}&=\frac{f(0)-f(-1)}{0-(-1)}\
&=\frac{4 - 11}{0 + 1}\
&=\frac{-7}{1}\
&=-7
\end{align*}
$$

# Answer:
$-7$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for average rate of change

Step2: Calculate \( f(-1) \)

Step3: Calculate \( f(0) \)

Step4: Apply the average rate of change formula

Answer: