sections 1.3 - 1.4
score: 4/21 answered: 4/21
question 5
find the average rate of change of ( f(x)=4 x^{2}-7 ) on the interval ( 5, t ). your answer will be an expression involving ( t )

Question

Accepted Answer

# Explanation:
## Step1: Recall the average rate of change formula
The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b=t$, and $f(x)=4x^{2}-7$.
## Step2: Calculate $f(5)$ and $f(t)$
- For $x = 5$, $f(5)=4\times5^{2}-7=4\times25 - 7=100 - 7=93$.
- For $x=t$, $f(t)=4t^{2}-7$.
## Step3: Substitute into the formula
$$
\begin{align*}
\frac{f(t)-f(5)}{t - 5}&=\frac{(4t^{2}-7)-93}{t - 5}\
&=\frac{4t^{2}-100}{t - 5}\
&=\frac{4(t^{2}-25)}{t - 5}\
&=\frac{4(t + 5)(t - 5)}{t - 5}\
&=4(t + 5)\
&=4t+20
\end{align*}
$$

# Answer:
$4t + 20$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the average rate of change formula

Step2: Calculate \(f(5)\) and \(f(t)\)

Step3: Substitute into the formula

Answer: