Question

Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval.

f(x)=x-2(sqrt x), interval [0,2]

Answer 1

f ' (c) = [ f ( b) - f ( a) ] / ( b -a)

Answer 2

@ashleynguyenx3 Where are you?

Answer 3

Sorry

Answer 4

Yes, I know.

Answer 5

I got the f(b) - F(a) part

Answer 6

Why would we need to find f'(x) I thought we'd find the anitderivative

Answer 7

Are you sure you comprehend the MVT?

Answer 8

Nope, my teacher didn't really go over it.

Answer 9

My book gives me the fomula

Answer 10

Find f ' (c)
Find f ( b) - f ( a) ] / ( b -a)
Equating them

Answer 11

@ashleynguyenx3 your formula is the same as @Chlorophyll 's if you take the derivative of both sides and use the fundamental theorem of calculus.

Answer 12

f'(c)= -2x
f(b) - f(a) / (b-a) = 0

Answer 13

Wait idk I'm doing.

Answer 14

I was looking at the wrong equation. So sorry.

Answer 15

f(0) = 0
f(2) = 2- 2\[\sqrt x\]

Answer 16

f(2) = 2 - 2(sqrt 2)

Answer 17

And then f'(c) = x - 3x^(3/2)

Answer 18

1 - 3x^(3/2)

Answer 19

4x^(3/2) / 3

Answer 20

Oh I get it, I did the antiderivative.

Answer 21

So my f'(c) = 1 - 2(1/ sqrt x)

Answer 22

2 sqrt x *

Answer 23

f ' ( c) = 1 - 1/sqrt x

Answer 24

Find f ' (c)
Find f ( b) - f ( a) ] / ( b -a)
Equating them

Answer 25

Okay, now I get it. You used the original MVT theorem.

Answer 26

Find c?

Answer 27

So I just set them equal to find the value of x, well c? But I don't understand how come my book says there are two answers.

Answer 28

chlorophyll and I apparently both misunderstood the question

Answer 29

I see, I skip the phrase " for integral" in your post!

Answer 30

So sorry about it!

Answer 31

No, I'm sorry.

Answer 32

So could you please explain it now?

Answer 33

What point you don't understand in the solution?

Answer 34

I don't think i understand where the factor if two goes between step 3 and 4 frankly :P

Answer 35

I don't understand after you solve the antiderivative and set it equal to f(c)(2-0)

Answer 36

I know it's the formula, but how do you solve it?

Answer 37

Since the concept is slope at specific point f'(c) = [ f(b) - f(a) ]/ ( b -a)
=> derivative for integral at x =c is f(c) ( b -a) = f(b) - f(a)

Answer 38

To be clear
F' (c) = [ F ( b) - F (a) ] / ( b -a)
f ( c) ( b -a ) = F ( b) - F (a)

Answer 39

Okay, I think I some what get it. From the the work that they show I just don't get how they got from
f(c)(2-0)=(6 - 8 sqrt 2)/3
to c - 2 sqrt c = ( 3 -4 sqrt 2)/3

Answer 40

f(x) = 2 - 2√x
->f (c) = 2 - 2√c

Answer 41

Then simplify both sides for 2: -> ( 3 -4 √2)

Answer 42

Nope, thank you! :)

Answer 43

Hundred % clear?

Answer 44

Not quite, but I think I'll get it eventually

Answer 45

AB, we're on a semester system so I'll be taking BC in January.

Answer 46

Wow, it's tough :s

Answer 47

Not to be mean, but I don't think my teacher is a good teacher.