Question

what is the exact difference between mean value theorem and average value when it comes to integration?

Answer 1

The average value of a derivative is the mean value of its underlying function. So if you have \(f(x)\) and its derivative \(f'(x)\), the average value of \(f'(x)\) is the mean value of \(f(x)\). In essence, this means that \(f'(x)\) between two points \(a) and \(b\) must at some point equal its own average value between those two points.

Answer 2

The average value formula, 1/(b-a) * Integral f(x)dx from a to b, gives the average y-value of function f between a and b. The mean value theorem (MVT) says take any smooth curve. Select two points on that curve and connect them with a straight line. MVT guarantees that somewhere between the two points, there will be a tangent line that is parallel to the line connecting the two points.

Answer 3

thanks guys, i finally get it!

Answer 4

Actually MVT of integration says that on (a, b) there exist a c such that f(c) = 1/(b-a) * Integral f(x)dx, and the proof is a lot easier than the derivative one

Answer 5

https://i.imgur.com/Wjmpc6D.png

Answer 6

Assessment items
Assessment started: undefined.
Item 1

Read the passage.

Dark Star

Giselle leaned against the mahogany bay horse, stroking the white diam

Answer 7

Okay I was gone for a minute BUT I'M BACK NOW

Answer 8

the scatter plot presents Ray's monthly electricity bills and amount of time ray

Answer 9

Which word shares a connotative meaning with the word cheap as it is used in this sentence?

Ashley thought her parents were being cheap when they bought ge

Answer 10

Which revision fixes the dangling modifier in the sentence?

Rowing through the rapids, the canoe began to fill with water.

Answer 11

dangling modifier

Answer 12

Misplaced Modifiers

Answer 13

For which literary work did Joseph Heller use his military experiences as a prima

Answer 14

Calc III Tutorial: Lagrange Multipliers

Answer 15

Can someone translate this for me?

Answer 16

Find the interest due on $1,090 at 8% for 5 years.

43.60
68.13
436.00
681.25

Answer 17

Now identify the simple subject and simple predicate.

The meeting began promptly at seven o'clock.

Answer 18

What can be inferred from these lines describing the pardoner in Chaucer's prolog

Answer 19

What is the rate of change of the linear relationship modeled in the table?

x y

Answer 20

Which of these best identifies the shift of mood in this sentence?

"If you were to sit more comfortably, you will not fall off.

Answer 21

Which scenario best matches the linear relationship expressed in the equation y = u221214x + 1,700?

Kent has $1,700 in his bank account and spends $14 each

Answer 22

The saying "Whoso is a man must be a nonconformist" is based on whose transcendentalist belief?
A.

Answer 23

Relationship A has a lesser rate than Relationship B. This table represents Relationship B.

Answer 24

Which person was a transcendentalist writer from Brooklyn, New York, who celebrat