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Tough Function Using Differentiation

  1. Apr 18, 2007 #1
    1. The problem statement, all variables and given/known data
    Find a function of the form f(x)=a+bcos(cx) that is tangent to the line y=1 at the point (0,1), and tangent to the line y=x+3/2-pi/4 at the point (pi/4, 3/2).


    2. Relevant equations
    I know that the problem involves differentiation and implicit differentiation. I don't really think there are many "equations" that I could give that would help, besides may the limit defintion.


    3. The attempt at a solution
    I haven't made it very far, but I am quite sure you need to somehow separate a, b, and c and than eliminate c altogether. I also have been trying odd and even values for c...
    all help is appreciated, thanks...
     
  2. jcsd
  3. Apr 18, 2007 #2

    CarlB

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    "Tangent at a point (a,b)" requires two degrees of freedom. The two curves have to both go through (a,b), and the two curves have to have the same deriviative.

    This means that you will get two equations for each "tangent at a point" restriction. You've got two such restrictions, so you should be able to get 2x2 = 4 equations from the tangent restrictions.

    There are only 3 unknown constants to solve for, a,b,c, so the problem might be over determined. In any case, this turns the problem from a calculus problem, which you are learning (i.e. find the slope of a curve), to an algebra problem (i.e. solve four equations in three unknowns) which you learned the technique in a previous class.

    So go for it!
     
  4. Apr 18, 2007 #3

    Dick

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    The tangency conditions give you requirements on the value of f(x) and f'(x) at various points. Write these equations down and if you are having problems people will try to help you. I'll get you started, f(0)=1.
     
  5. Apr 18, 2007 #4
    thanks for the help so far...
     
  6. Jun 23, 2009 #5
    y= 3/2 - (1/2)cos(2x)
     
  7. Jun 23, 2009 #6

    Dick

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    You are i) violating the forum rules by supplying an solution instead of hints on how to solve it (even if it is right, which I haven't checked) and ii) this thread is two years old. What's your point?
     
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