anonymous
  • anonymous
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]
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
@Mertsj can u help?
anonymous
  • anonymous
@experimentX how would i do this one?
experimentX
  • experimentX
let f(x) = sin(x) then f'(x) = ?

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anonymous
  • anonymous
okay
anonymous
  • anonymous
cos(x)
experimentX
  • experimentX
when is cos(x) zero?
anonymous
  • anonymous
zero? you said find the derivative of sinx right?
experimentX
  • experimentX
yes ... at what point is cos(x) equal to zero?
anonymous
  • anonymous
there is not point where it is equal to zero
experimentX
  • experimentX
why not?
anonymous
  • anonymous
when i graph it...it doesn't
experimentX
  • experimentX
you got the wrong graph then.
anonymous
  • anonymous
|dw:1363197320465:dw| thats how it looks liek ohh okay
experimentX
  • experimentX
|dw:1363197334937:dw|
anonymous
  • anonymous
ok
experimentX
  • experimentX
|dw:1363197397226:dw|
anonymous
  • anonymous
yea it is
anonymous
  • anonymous
okay i got it
experimentX
  • experimentX
so ... what's the point?
anonymous
  • anonymous
(0,1) ?
experimentX
  • experimentX
no ...
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=plot+cos%28x%29+from+-2pi+to+2pi
anonymous
  • anonymous
so its more than 1?
anonymous
  • anonymous
0,1.5 ?
experimentX
  • experimentX
NOOOOOOOOOOOOOOO http://www.wolframalpha.com/input/?i=solve+cos%28x%29+%3D+0+for+x+between+0+and+pi
anonymous
  • anonymous
so its 1.57080?
experimentX
  • experimentX
|dw:1363198158808:dw|
anonymous
  • anonymous
ok
experimentX
  • experimentX
so pick any two points above pi/2 and below pi/2
anonymous
  • anonymous
okay? do you do this different than the las tone tho? i'm not gonna use f(a) - f(b)/ b - a ?
experimentX
  • experimentX
|dw:1363198343133:dw|
anonymous
  • anonymous
ohh ok
experimentX
  • experimentX
|dw:1363198401986:dw|
anonymous
  • anonymous
ok
experimentX
  • experimentX
|dw:1363198546707:dw| do you get that?
anonymous
  • anonymous
yes i do
experimentX
  • experimentX
Okay i gotta go ...
anonymous
  • anonymous
ok thx
experimentX
  • experimentX
|dw:1363198676612:dw|
anonymous
  • anonymous
okay
anonymous
  • 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
  • anonymous
f(3pi/4) = 3pi^2 + 1 = ?
anonymous
  • anonymous
can u tell me if i plugged it right @experimentX ?
experimentX
  • experimentX
yes that's correct.
experimentX
  • 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
  • anonymous
okay
anonymous
  • anonymous
I got 1
experimentX
  • experimentX
huh .. do it again, what is sin(pi/4) ... plug into wolfram.
anonymous
  • anonymous
hold on
anonymous
  • anonymous
1/sqrt(2)
anonymous
  • anonymous
i got 1 over sqrt of 2
anonymous
  • anonymous
what do i do next ?
experimentX
  • experimentX
yes ... plug into your Rolle's condition.
anonymous
  • anonymous
the formula right?
anonymous
  • anonymous
so f(1/sqrt(2) - f(1/sqrt(2)/ 1/sqrt(2) - 1/sqrt(2) ?
experimentX
  • experimentX
no ...
experimentX
  • experimentX
|dw:1363384214639:dw|
anonymous
  • anonymous
ohh ok
anonymous
  • anonymous
how do i solve that?
anonymous
  • anonymous
so it will be 3/3 right?
experimentX
  • experimentX
|dw:1363384415083:dw|
anonymous
  • anonymous
okay
anonymous
  • anonymous
so those will be the numerator?
experimentX
  • experimentX
yes ... you just found out the value. Do you know what is functional notation?
anonymous
  • anonymous
no
experimentX
  • 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
  • anonymous
f(x) = 1
experimentX
  • experimentX
yep ... if f(x) = sin(x) ,,, then what is f(pi/4) ??
anonymous
  • anonymous
1 over sqrt(2)
experimentX
  • experimentX
yes ... what is f(3pi/4) ??
anonymous
  • anonymous
its the same 1 over sqrt(2)
experimentX
  • experimentX
yes ... plug in those values in |dw:1363385976116:dw|
anonymous
  • anonymous
plug them in the denominator?
experimentX
  • experimentX
|dw:1363386098600:dw|
anonymous
  • anonymous
ohh okay hold on
anonymous
  • anonymous
f(1/sqrt(2) - f(1/sqrt(2) over 3pi/4 - pi/4
experimentX
  • experimentX
No no ... what are you dong?? why are you putting 1/sqrt(2) inside function?
anonymous
  • anonymous
you said to plug them in?
experimentX
  • experimentX
yes .. |dw:1363386528821:dw|
anonymous
  • anonymous
okay
anonymous
  • anonymous
i'll ask my teacher on this one thanks for your help.
experimentX
  • experimentX
|dw:1363387122187:dw|
anonymous
  • anonymous
so i plug those in pi?
experimentX
  • experimentX
no ... you just calculated those values. plug them in.
anonymous
  • anonymous
I just did and you told me it was incorrect..i'm confused
experimentX
  • experimentX
yes ... this is where you got confused.
anonymous
  • anonymous
ok
experimentX
  • experimentX
|dw:1363387985440:dw|
anonymous
  • anonymous
ohh ok
experimentX
  • experimentX
what is the value of|dw:1363388256685:dw|
anonymous
  • anonymous
0?
experimentX
  • experimentX
yes ... so |dw:1363388362361:dw|
anonymous
  • anonymous
the derivative of it?
experimentX
  • experimentX
yes ... is there a point where derivative is zero?
anonymous
  • anonymous
yea
experimentX
  • experimentX
what is that point?
anonymous
  • anonymous
umm at 0, 0?
experimentX
  • experimentX
No ..
anonymous
  • anonymous
idk
experimentX
  • experimentX
we talked about that in the above posts. check again ... the point is pi/2
anonymous
  • anonymous
ohh yes okay
anonymous
  • anonymous
so it reached 0 at pi/2
experimentX
  • experimentX
no ... the derivative is zero at pi/2
anonymous
  • anonymous
ok
experimentX
  • experimentX
gotta go ... you gotta work harder.
experimentX
  • experimentX
good luck!!
anonymous
  • anonymous
ok well can u tell me what i should do next before you go
experimentX
  • experimentX
you wanted to verify Rolle's theorem, which you did.
anonymous
  • anonymous
yea its continuos and differentiable i know that
experimentX
  • experimentX
what do you want to do?
anonymous
  • anonymous
find a value for c
anonymous
  • anonymous
so this could be true a < c < b
experimentX
  • experimentX
of course it is ..
experimentX
  • experimentX
|dw:1363389508215:dw|
anonymous
  • anonymous
ok so c is pi/2 ?
experimentX
  • experimentX
|dw:1363389556563:dw|
anonymous
  • anonymous
ohhh ok
anonymous
  • anonymous
so c is 2pi/4
experimentX
  • experimentX
yes
anonymous
  • anonymous
ok
experimentX
  • experimentX
any probs??
anonymous
  • anonymous
no thx
experimentX
  • experimentX
see you around ... gotta go offline :)
anonymous
  • anonymous
ok

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