clara1223
  • clara1223
Determine if the Mean Value Theorem applies to the function f(x)=2sin(x)+sin(2x) on the interval [0,pi]. If so, find all numbers c on the interval that satisfy the theorem.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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zepdrix
  • zepdrix
Which one is the Mean Value Theorem again? Oh right right right.. the one with the uhhhh... You have some interval... With the `secant line` connecting the end points... Mean Value Theorem tells us that there is a `tangent line` somewhere inside of that interval. So ummm
clara1223
  • clara1223
yeah so you have to find (f(pi)-f(0))/(pi-0)
clara1223
  • clara1223
and then set that equal to the derivative of the function

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clara1223
  • clara1223
i just have trouble with trig on this kind of problem
ganeshie8
  • ganeshie8
how do you know MVT can be applied here? have you shown that the given function meets the requirements necessary for applying MVT ? |dw:1444089635169:dw|
clara1223
  • clara1223
I graphed it and it is continuous and differentiable on the interval
ganeshie8
  • ganeshie8
Fair enough! now you're ready to apply MVT
ganeshie8
  • ganeshie8
As a start, find the slope of secant line of f(x)=2sin(x)+sin(2x) between [0,pi]
ganeshie8
  • ganeshie8
f(x)=2sin(x)+sin(2x) f(pi) = 0 f(0) = 0 so, clearly (f(pi)-f(0))/(pi-0) = 0
ganeshie8
  • ganeshie8
so, you want to solve \[2\cos(c)+\cos(2c)=0\] over the interval \((0,\pi)\)
ganeshie8
  • ganeshie8
recall the identity : \(\cos(2x)=2\cos^2x-1\)
clara1223
  • clara1223
and how do i use that identity?
ganeshie8
  • ganeshie8
\(2\cos(c)+2\cos(2c)=0\) \(\cos(c)+\cos(2c)=0\) Applying double angle identity : \(\cos(c)+2\cos^2(c)-1=0\) \(2\cos^2(c)+\cos(c)-1=0\) Try factoring it

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