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

Math help

Answer 6

Math help

Answer 7

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers.

Answer 8

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Answer 9

Math help

Answer 10

Math help please

Answer 11

For the graph, which are possible functions u0192 and g?

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Answer 12

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Answer 13

Select the correct answer.
Read this excerpt from "The Third Philippic," written by Demosthenes in 342 B.

Answer 14

Jackson is teaching a class the concept of the binary number system. Which term w

Answer 15

Affirmative action policies were originally designed to _____.

make sure a certa

Answer 16

What two Democratic leaders constantly challenged President Carter during his adm

Answer 17

Is the function u0192(x) = xu2078 an exponential function? If so, identify the base.

Answer 18

Perform the arithmetic operation. Write it in the simplest form. 5 yd. 1 ft. - 2 yd.

Answer 19

The narrator's description of Kunthi as "a thin, slight girl" connotes that

Answer 20

Math help

Answer 21

I just write whatever comes to mind, so..ye.

- Endless -

Answer 22

Which term describes the point where the perpendicular bisectors of the three sid

Answer 23

Write the Standard Form of the line with x-intercept of 3 and y-intercept of 4.

Answer 24

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