a pancake company uses the function (f(x)=1.5x^{2}) to calculate the number of calories in a pancake with a…
a pancake company uses the function (f(x)=1.5x^{2}) to calculate the number of calories in a pancake with a diameter of (x) cm. what is the average rate of change for the function over the interval (10 < x < 12)?\na. 150 calories per cm of diameter\nb. 33 calories per cm of diameter\nc. 65 calories per cm of diameter\nd. 215 calories per cm of diameter
Answer
Explanation:
Step1: Recall 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, $a = 10$, $b = 12$, and $f(x)=1.5x^{2}$.
Step2: Calculate $f(12)$
Substitute $x = 12$ into $f(x)$: $f(12)=1.5\times12^{2}=1.5\times144 = 216$.
Step3: Calculate $f(10)$
Substitute $x = 10$ into $f(x)$: $f(10)=1.5\times10^{2}=1.5\times100 = 150$.
Step4: Calculate average rate of change
$\frac{f(12)-f(10)}{12 - 10}=\frac{216 - 150}{2}=\frac{66}{2}=33$.
Answer:
B. 33 calories per cm of diameter