Check the hypotheses of Rolle’s Theorem and the Mean Value Theorem and find a value of c that makes the appropriate conclusion true. Illustrate the conclusion with a graph. f(x) = sin x , [0,pi/2]

- anonymous

- katieb

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- anonymous

@Mertsj can u help?

- anonymous

@experimentX how would i do this one?

- experimentX

let f(x) = sin(x)
then f'(x) = ?

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## More answers

- anonymous

okay

- anonymous

cos(x)

- experimentX

when is cos(x) zero?

- anonymous

zero? you said find the derivative of sinx right?

- experimentX

yes ... at what point is cos(x) equal to zero?

- anonymous

there is not point where it is equal to zero

- experimentX

why not?

- anonymous

when i graph it...it doesn't

- experimentX

you got the wrong graph then.

- anonymous

|dw:1363197320465:dw| thats how it looks liek ohh okay

- experimentX

|dw:1363197334937:dw|

- anonymous

ok

- experimentX

|dw:1363197397226:dw|

- anonymous

yea it is

- anonymous

okay i got it

- experimentX

so ... what's the point?

- anonymous

(0,1) ?

- experimentX

no ...

- experimentX

http://www.wolframalpha.com/input/?i=plot+cos%28x%29+from+-2pi+to+2pi

- anonymous

so its more than 1?

- anonymous

0,1.5 ?

- experimentX

NOOOOOOOOOOOOOOO
http://www.wolframalpha.com/input/?i=solve+cos%28x%29+%3D+0+for+x+between+0+and+pi

- anonymous

so its 1.57080?

- experimentX

|dw:1363198158808:dw|

- anonymous

ok

- experimentX

so pick any two points above pi/2 and below pi/2

- anonymous

okay? do you do this different than the las tone tho? i'm not gonna use f(a) - f(b)/ b - a ?

- experimentX

|dw:1363198343133:dw|

- anonymous

ohh ok

- experimentX

|dw:1363198401986:dw|

- anonymous

ok

- experimentX

|dw:1363198546707:dw|
do you get that?

- anonymous

yes i do

- experimentX

Okay i gotta go ...

- anonymous

ok thx

- experimentX

|dw:1363198676612:dw|

- anonymous

okay

- anonymous

So i filled in those a b c's and here i got....f(pi/2) = f(3pi/4) - f(pi/4) over 3pi/4 - pi/4

- anonymous

f(3pi/4) = 3pi^2 + 1 = ?

- anonymous

can u tell me if i plugged it right @experimentX ?

- experimentX

yes that's correct.

- experimentX

\[ f(3 \pi /4) = \sin(3\pi/4) = 1/ \sqrt 2 \]
Find the value of f(pi/4) from your calculator or wolfram.

- anonymous

okay

- anonymous

I got 1

- experimentX

huh .. do it again, what is sin(pi/4) ... plug into wolfram.

- anonymous

hold on

- anonymous

1/sqrt(2)

- anonymous

i got 1 over sqrt of 2

- anonymous

what do i do next ?

- experimentX

yes ... plug into your Rolle's condition.

- anonymous

the formula right?

- anonymous

so f(1/sqrt(2) - f(1/sqrt(2)/ 1/sqrt(2) - 1/sqrt(2) ?

- experimentX

no ...

- experimentX

|dw:1363384214639:dw|

- anonymous

ohh ok

- anonymous

how do i solve that?

- anonymous

so it will be 3/3 right?

- experimentX

|dw:1363384415083:dw|

- anonymous

okay

- anonymous

so those will be the numerator?

- experimentX

yes ... you just found out the value. Do you know what is functional notation?

- anonymous

no

- experimentX

yeah ... that is the problem. you haven't advanced to the point of doing this.
let f(x) = cos(x), what is value of f(0)

- anonymous

f(x) = 1

- experimentX

yep ...
if f(x) = sin(x) ,,, then what is f(pi/4) ??

- anonymous

1 over sqrt(2)

- experimentX

yes ... what is f(3pi/4) ??

- anonymous

its the same 1 over sqrt(2)

- experimentX

yes ... plug in those values in |dw:1363385976116:dw|

- anonymous

plug them in the denominator?

- experimentX

|dw:1363386098600:dw|

- anonymous

ohh okay hold on

- anonymous

f(1/sqrt(2) - f(1/sqrt(2) over 3pi/4 - pi/4

- experimentX

No no ... what are you dong?? why are you putting 1/sqrt(2) inside function?

- anonymous

you said to plug them in?

- experimentX

yes .. |dw:1363386528821:dw|

- anonymous

okay

- anonymous

i'll ask my teacher on this one thanks for your help.

- experimentX

|dw:1363387122187:dw|

- anonymous

so i plug those in pi?

- experimentX

no ... you just calculated those values. plug them in.

- anonymous

I just did and you told me it was incorrect..i'm confused

- experimentX

yes ... this is where you got confused.

- anonymous

ok

- experimentX

|dw:1363387985440:dw|

- anonymous

ohh ok

- experimentX

what is the value of|dw:1363388256685:dw|

- anonymous

0?

- experimentX

yes ... so |dw:1363388362361:dw|

- anonymous

the derivative of it?

- experimentX

yes ... is there a point where derivative is zero?

- anonymous

yea

- experimentX

what is that point?

- anonymous

umm at 0, 0?

- experimentX

No ..

- anonymous

idk

- experimentX

we talked about that in the above posts. check again ... the point is pi/2

- anonymous

ohh yes okay

- anonymous

so it reached 0 at pi/2

- experimentX

no ... the derivative is zero at pi/2

- anonymous

ok

- experimentX

gotta go ... you gotta work harder.

- experimentX

good luck!!

- anonymous

ok well can u tell me what i should do next before you go

- experimentX

you wanted to verify Rolle's theorem, which you did.

- anonymous

yea its continuos and differentiable i know that

- experimentX

what do you want to do?

- anonymous

find a value for c

- anonymous

so this could be true a < c < b

- experimentX

of course it is ..

- experimentX

|dw:1363389508215:dw|

- anonymous

ok so c is pi/2 ?

- experimentX

|dw:1363389556563:dw|

- anonymous

ohhh ok

- anonymous

so c is 2pi/4

- experimentX

yes

- anonymous

ok

- experimentX

any probs??

- anonymous

no thx

- experimentX

see you around ... gotta go offline :)

- anonymous

ok

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