Question

Find the average rate of change of f(x)=7x ² −9 on the interval [2,b]. Your answer will be an expression involving b.

a. b²-4/b-2
b. 14b-8
c. 7b-9
d. 14b/b+2

Answer 1

The average rate of change of the function f(x) = 7x² - 9 on the interval [2, b] is calculated by using the formula for the average rate of change and simplifying the expression, resulting in the answer 14b - 8.

Step-by-step explanation:

To find the average rate of change of the function f(x) = 7x² − 9 on the interval [2, b], we need to use the formula:

Average Rate of Change = rac{f(b) - f(a)}{b - a}

First, we calculate the values of the function at the endpoints of the interval:

• f(2) = 7(2)^2 - 9 = 28 - 9 = 19
• f(b) = 7(b)^2 - 9

Now, we apply the formula for average rate of change:

Average Rate of Change = rac{7(b)^2 - 9 - 19}{b - 2}

Simplify the numerator:

Average Rate of Change = rac{7b^2 - 9 - 19}{b - 2}

Average Rate of Change = rac{7b^2 - 28}{b - 2}

Then, factor out a 7 from the numerator:

Average Rate of Change = rac{7(b^2 - 4)}{b - 2}

Thus, the average rate of change of f(x) from x = 2 to x = b is 14b - 8, which corresponds to answer choice (b).