Question

suppose that f(t)=t^2 + 3t - 2. what is the average rate of change of f(t) over the interval 5 to 6? the average rate of change of f(t) over the interval 5 to 6 is

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(t)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 5$, $b = 6$, and $f(t)=t^{2}+3t - 2$.

Step2: Calculate $f(6)$

Substitute $t = 6$ into $f(t)$:
$f(6)=6^{2}+3\times6 - 2=36 + 18-2=52$.

Step3: Calculate $f(5)$

Substitute $t = 5$ into $f(t)$:
$f(5)=5^{2}+3\times5 - 2=25+15 - 2=38$.

Step4: Calculate the average rate of change

Using the formula $\frac{f(6)-f(5)}{6 - 5}$, we have $\frac{52 - 38}{1}=14$.

Answer:

$14$