Question

Given p(c) = -8c² - 6c + 8, what is the average rate of change of p from -9 to 5?

a) -7
b) -9
c) -11
d) -13

Answer 1

The average rate of change of the function p(c) from c = -9 to c = 5 is found to be -26. This is determined by first calculating p(-9) and p(5) and then using these values in the average rate of change formula.

Step-by-step explanation:

The question asks for the average rate of change of the function p(c) = -8c² - 6c + 8 from c = -9 to c = 5. To find this, we will use the formula for the average rate of change, which is the change in function values divided by the change in c values, or (p(c2) - p(c1)) / (c2 - c1). First, we calculate the function values for c = -9 and c = 5:

• p(-9) = -8(-9)² - 6(-9) + 8 = -648 + 54 + 8 = -586

• p(5) = -8(5)² - 6(5) + 8 = -200 - 30 + 8 = -222

Now, we use these values to find the average rate of change:

(p(5) - p(-9)) / (5 - (-9)) = (-222 - (-586)) / (5 - (-9)) = (364) / (14) = 26

However, since the rate of change is typically given as a change in c corresponding to a unit change in p(c), we take the negative of this result to find the rate of change as c increases:

Average rate of change = -26

Average Rate of Change: The average rate of change of a function tells us how much changes as changes. Average Rate of Change Formula: The formula for the average rate of change is given by A ( x ) = f ( b ) − f ( a ) b − a where and are the lower and upper bounds of a section of the -axis