Find the average value of the function f over the interval [2, 7].

Question

f(x) = 10 − x

Answer 1

Average value of a function =1/(b-a) times the integral from a to b of the function.

7

f _avg = 1/(7-2) times ∫ (10-x)dx.

2

1/5 times (10x - x²/2)evaluated from 2 to 7

1/5 [(70-49/2)-(20-2)]

Answer: 11/2

Answer 2

Hello Gabrielle

The average value of a function over a specific interval is the change in the function during that interval divided by the interval.

Think of it as drawing a straight line from one end point {f(2)} to the other end point {f(7)] and finding the slope of that line.

Hence, for this problem the average value is [ f(7) - f(2)]/ (7-2) -- i.e rise over run.

I get (-1)