Question

a burrito company uses the function $c(x)=1.74x^2$ to calculate the number of calories in a tortilla with a diameter of $x$ inches.
a. find the average rate of change of the function over the intervals $6 < x < 8$ and $9 < x < 11$.
b. interpret the average rates of change.
c. what does the difference in the average rates of change mean in terms of the situation?

a. the average rate of change of $c(x)$ over $6 < x < 8$ is $square$
(simplify your answer type an integer or a decimal )

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function \( C(x) \) over the interval \( a < x < b \) is given by \( \frac{C(b) - C(a)}{b - a} \).

Step2: Calculate \( C(6) \) and \( C(8) \)

First, find \( C(6) \):
\( C(6)=1.74\times(6)^{2}=1.74\times36 = 62.64 \)
Then, find \( C(8) \):
\( C(8)=1.74\times(8)^{2}=1.74\times64 = 111.36 \)

Step3: Compute average rate of change for \( 6 < x < 8 \)

Using the formula \( \frac{C(8)-C(6)}{8 - 6} \), substitute the values:
\( \frac{111.36 - 62.64}{2}=\frac{48.72}{2}=24.36 \)

Answer:

24.36