Find the average value of the function over the given interval.
-f(x) = -2x + 8 on [-8, 4]
A) 24
B) 12
C) 4
D) 144

Question

Quizplus · Accepted Answer

The average value of a function over an interval is given by the formula:
average value = 1/(b-a) * integral from a to b of f(x) dx
Applying this formula to the given function on the interval [-8,4], we get:
average value = 1/(4-(-8)) * integral from -8 to 4 of (-2x+8) dx
= 1/12 * [-x^2 + 8x] from -8 to 4
= 1/12 * [(16-32) - (-64+64)]
= 1/12 * 16
= 4/3
Therefore, the average value of the function over the interval [-8,4] is 4/3 or approximately 1.33. The closest answer choice is B, 12, which is equal to 3*4, so the answer is B.

Find the Average Value of the Function Over the Given