Question
calculate the average rate of change over [2,4] given the function table for f(x)=-x^2+12.
step by step
step by step
Answers
GPT 3.5
1. Find the value of f(2) and f(4) using the function table:
f(2) = -(2)^2 + 12 = -4 + 12 = 8
f(4) = -(4)^2 + 12 = -16 + 12 = -4
2. Calculate the average rate of change by using the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
3. Substitute the values of f(4) = -4 and f(2) = 8 into the formula:
Average Rate of Change = (-4 - 8) / (4 - 2)
Average Rate of Change = -12 / 2
Average Rate of Change = -6
Therefore, the average rate of change over [2,4] for the function f(x) = -x^2 + 12 is -6.
f(2) = -(2)^2 + 12 = -4 + 12 = 8
f(4) = -(4)^2 + 12 = -16 + 12 = -4
2. Calculate the average rate of change by using the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
3. Substitute the values of f(4) = -4 and f(2) = 8 into the formula:
Average Rate of Change = (-4 - 8) / (4 - 2)
Average Rate of Change = -12 / 2
Average Rate of Change = -6
Therefore, the average rate of change over [2,4] for the function f(x) = -x^2 + 12 is -6.