Question

need help on attachment

Answer 1

well we know f(a)=f(b)

Answer 2

and its is continuse on the interval [0,6]

Answer 3

and since it is contiuose on that interval then it also is differntiable in the interval (0,6)

Answer 4

its xsqrt(6-x)

Answer 5

So the only thing we have to determime the citical values of the function or at what value the derivative is zero

Answer 6

have you dtermined the derivaitve

Answer 7

no that just what the original function is, but the attachment didn't show the minus sign inside the square root

Answer 8

yes it did

Answer 9

oh, well then

Answer 10

but do you understand that you have to get the derivaitve of this function first and can you do that?

Answer 11

yes

Answer 12

so, then why did you post this question if you know how to do it already?

Answer 13

just know if I doing right, so I got 3(4-x)/2sqrt(6-x) for the derivative

Answer 14

is it right?

Answer 15

looks good to me

Answer 16

now all you have to do is find that "C" that makes the derivaitve 0

Answer 17

so how would you do that?

Answer 18

well, the derivative is zero when: 3(4-x)=0, right?

Answer 19

yes so x=4

Answer 20

you are correct

Answer 21

what about the bottom 2sqrt(6-x) is that x=6?

Answer 22

we dont concern ourselves with when the denominator is zero, because that would result make the derivative undefined

Answer 23

so its undefined at x=6?

Answer 24

also if you think about it logicallly none of your choices has a 6 in it

Answer 25

so when finding the critical points we are only concern with the numerator, correct?

Answer 26

when finding the critical point we concern ourselves with when the derivative is zero

Answer 27

but when the critical point is on denominator its undefined always, but do we still count it as a critical point?

Answer 28

well, critical points are those points where f'(x) if 0 or f'(x) is undefined

Answer 29

oh, but since this problem is rolle theorem problem its what f'(X) to be 0 and exist

Answer 30

and not be f'(x) to be undefined

Answer 31

yes, thats why i said we concern ourselves with only when the numerator was zero

Answer 32

if we had been taking in account when the denomintor was zero, then the question would not have been asking us to verify rolles theorem

Answer 33

ok so just something of topic is the derivative of f(X)=cosx-sin^2(x), is f'(x)=-sinx(2cosx+1)

Answer 34

oops I meant off topic

Answer 35

but in general, when you get to the first derivaitve test then you do need to take into account when the derivative is undefined

Answer 36

ok

Answer 37

it should be :
-sin(x)-2(sin(x))(cos(x))

Answer 38

what would the critical points be on a closed interval from 1, 2pi

Answer 39

i would say pi

Answer 40

and 0

Answer 41

oops! I meant closed interval from 0, 2pi

Answer 42

and 2pi

Answer 43

yeah would it be pi/3, pi, 5pi/3

Answer 44

0,pi,2pi

Answer 45

if you dont believe me plug in the values you have evaluate the derivaitve ans see if you get zero at those values

Answer 46

i cant open it

Answer 47

can you open now

Answer 48

no

Answer 49

like i said thoug, you have to find when those trig functions are zero

Answer 50

or when that derivaitve results in zero

Answer 51

set the derivaitve to zero and find the critical points

Answer 52

i got 0,pi, and 2pi

Answer 53

that not one of the answer choices listed on the attachment

Answer 54

okay i got it