For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by the formula av(f) =- b-a f(x) dx. Do f and the constant function av(f) have a b b the same integral over [a,b]? That is, does av(f) dx = | f(x) dx? Give reasons for your answer. Do f and av(f) have the same integral over [a,b]? Choose the correct answer below. O A. Yes, the function f must equal av(f) for at least one value of x in [a,b]. b b 1 O B. No, since av(f) = f(x) dx, and the integral of f over [a,b] is f(x) dx, the two integrals differ by a factor of f)%3D b-a b-a a a OC. No, only when f is equal to the constant function av(f) are the two integrals equal. b O D. Yes, let f(x) dx = A. Then av(f) = A The integral of this constant over [a,b] is A. b-a
For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by the formula av(f) =- b-a f(x) dx. Do f and the constant function av(f) have a b b the same integral over [a,b]? That is, does av(f) dx = | f(x) dx? Give reasons for your answer. Do f and av(f) have the same integral over [a,b]? Choose the correct answer below. O A. Yes, the function f must equal av(f) for at least one value of x in [a,b]. b b 1 O B. No, since av(f) = f(x) dx, and the integral of f over [a,b] is f(x) dx, the two integrals differ by a factor of f)%3D b-a b-a a a OC. No, only when f is equal to the constant function av(f) are the two integrals equal. b O D. Yes, let f(x) dx = A. Then av(f) = A The integral of this constant over [a,b] is A. b-a
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by the formula av(f) =-
b-a
f(x) dx. Do f and the constant function av(f) have
a
b
b
the same integral over [a,b]? That is, does
av(f) dx = | f(x) dx? Give reasons for your answer.
Do f and av(f) have the same integral over [a,b]? Choose the correct answer below.
O A. Yes, the function f must equal av(f) for at least one value of x in [a,b].
b
b
1
O B. No, since av(f) = f(x) dx, and the integral of f over [a,b] is f(x) dx, the two integrals differ by a factor of
f)%3D
b-a
b-a
a
a
OC. No, only when f is equal to the constant function av(f) are the two integrals equal.
b
O D. Yes, let f(x) dx = A. Then av(f) =
A
The integral of this constant over [a,b] is A.
b-a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d160791-4f18-48d0-9d89-545079aa2ea5%2Faf82dd53-e79f-4c33-a0c2-807efa0a6e61%2Fvonzsz_processed.png&w=3840&q=75)
Transcribed Image Text:For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by the formula av(f) =-
b-a
f(x) dx. Do f and the constant function av(f) have
a
b
b
the same integral over [a,b]? That is, does
av(f) dx = | f(x) dx? Give reasons for your answer.
Do f and av(f) have the same integral over [a,b]? Choose the correct answer below.
O A. Yes, the function f must equal av(f) for at least one value of x in [a,b].
b
b
1
O B. No, since av(f) = f(x) dx, and the integral of f over [a,b] is f(x) dx, the two integrals differ by a factor of
f)%3D
b-a
b-a
a
a
OC. No, only when f is equal to the constant function av(f) are the two integrals equal.
b
O D. Yes, let f(x) dx = A. Then av(f) =
A
The integral of this constant over [a,b] is A.
b-a
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