onegirl
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]
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onegirl
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@Mertsj can u help?
onegirl
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@experimentX how would i do this one?
experimentX
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let f(x) = sin(x)
then f'(x) = ?
onegirl
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okay
onegirl
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cos(x)
experimentX
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when is cos(x) zero?
onegirl
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zero? you said find the derivative of sinx right?
experimentX
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yes ... at what point is cos(x) equal to zero?
onegirl
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there is not point where it is equal to zero
experimentX
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why not?
onegirl
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when i graph it...it doesn't
experimentX
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you got the wrong graph then.
onegirl
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|dw:1363197320465:dw| thats how it looks liek ohh okay
experimentX
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|dw:1363197334937:dw|
onegirl
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ok
experimentX
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|dw:1363197397226:dw|
onegirl
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yea it is
onegirl
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okay i got it
experimentX
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so ... what's the point?
onegirl
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(0,1) ?
experimentX
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no ...
onegirl
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so its more than 1?
onegirl
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0,1.5 ?
onegirl
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so its 1.57080?
experimentX
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|dw:1363198158808:dw|
onegirl
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ok
experimentX
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so pick any two points above pi/2 and below pi/2
onegirl
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okay? do you do this different than the las tone tho? i'm not gonna use f(a) - f(b)/ b - a ?
experimentX
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|dw:1363198343133:dw|
onegirl
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ohh ok
experimentX
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|dw:1363198401986:dw|
onegirl
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ok
experimentX
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|dw:1363198546707:dw|
do you get that?
onegirl
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yes i do
experimentX
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Okay i gotta go ...
onegirl
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ok thx
experimentX
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|dw:1363198676612:dw|
onegirl
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okay
onegirl
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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
onegirl
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f(3pi/4) = 3pi^2 + 1 = ?
onegirl
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can u tell me if i plugged it right @experimentX ?
experimentX
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yes that's correct.
experimentX
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\[ f(3 \pi /4) = \sin(3\pi/4) = 1/ \sqrt 2 \]
Find the value of f(pi/4) from your calculator or wolfram.
onegirl
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okay
onegirl
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I got 1
experimentX
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huh .. do it again, what is sin(pi/4) ... plug into wolfram.
onegirl
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hold on
onegirl
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1/sqrt(2)
onegirl
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i got 1 over sqrt of 2
onegirl
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what do i do next ?
experimentX
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yes ... plug into your Rolle's condition.
onegirl
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the formula right?
onegirl
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so f(1/sqrt(2) - f(1/sqrt(2)/ 1/sqrt(2) - 1/sqrt(2) ?
experimentX
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no ...
experimentX
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|dw:1363384214639:dw|
onegirl
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ohh ok
onegirl
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how do i solve that?
onegirl
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so it will be 3/3 right?
experimentX
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|dw:1363384415083:dw|
onegirl
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okay
onegirl
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so those will be the numerator?
experimentX
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yes ... you just found out the value. Do you know what is functional notation?
onegirl
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no
experimentX
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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)
onegirl
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f(x) = 1
experimentX
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yep ...
if f(x) = sin(x) ,,, then what is f(pi/4) ??
onegirl
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1 over sqrt(2)
experimentX
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yes ... what is f(3pi/4) ??
onegirl
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its the same 1 over sqrt(2)
experimentX
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yes ... plug in those values in |dw:1363385976116:dw|
onegirl
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plug them in the denominator?
experimentX
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|dw:1363386098600:dw|
onegirl
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ohh okay hold on
onegirl
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f(1/sqrt(2) - f(1/sqrt(2) over 3pi/4 - pi/4
experimentX
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No no ... what are you dong?? why are you putting 1/sqrt(2) inside function?
onegirl
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you said to plug them in?
experimentX
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yes .. |dw:1363386528821:dw|
onegirl
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okay
onegirl
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i'll ask my teacher on this one thanks for your help.
experimentX
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|dw:1363387122187:dw|
onegirl
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so i plug those in pi?
experimentX
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no ... you just calculated those values. plug them in.
onegirl
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I just did and you told me it was incorrect..i'm confused
experimentX
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yes ... this is where you got confused.
onegirl
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ok
experimentX
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|dw:1363387985440:dw|
onegirl
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ohh ok
experimentX
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what is the value of|dw:1363388256685:dw|
onegirl
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0?
experimentX
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yes ... so |dw:1363388362361:dw|
onegirl
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the derivative of it?
experimentX
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yes ... is there a point where derivative is zero?
onegirl
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yea
experimentX
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what is that point?
onegirl
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umm at 0, 0?
experimentX
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No ..
onegirl
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idk
experimentX
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we talked about that in the above posts. check again ... the point is pi/2
onegirl
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ohh yes okay
onegirl
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so it reached 0 at pi/2
experimentX
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no ... the derivative is zero at pi/2
onegirl
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ok
experimentX
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gotta go ... you gotta work harder.
experimentX
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good luck!!
onegirl
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ok well can u tell me what i should do next before you go
experimentX
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you wanted to verify Rolle's theorem, which you did.
onegirl
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yea its continuos and differentiable i know that
experimentX
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what do you want to do?
onegirl
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find a value for c
onegirl
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so this could be true a < c < b
experimentX
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of course it is ..
experimentX
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|dw:1363389508215:dw|
onegirl
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ok so c is pi/2 ?
experimentX
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|dw:1363389556563:dw|
onegirl
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ohhh ok
onegirl
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so c is 2pi/4
experimentX
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yes
onegirl
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ok
experimentX
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any probs??
onegirl
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no thx
experimentX
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see you around ... gotta go offline :)
onegirl
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ok