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Math Help - Find the equation

  1. #1
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    Find the equation

    Consider the curves in the first quadrant that have equations
    where is a positive constant.
    Different values of give different curves. The curves form a family, .
    Let Let be the member of the family that goes through P.
    A. Let be the equation of . Find .
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  2. #2
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    Well? You are told that the equation is of the form y= Aexp(4x) and that its graph goes through (2, 2). y= 2= A exp(4(2))= A exp(8). what is A?
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  3. #3
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    ln(2)/8???
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  4. #4
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    Quote Originally Posted by amiv4 View Post
    ln(2)/8???
    A = \frac{2}{\exp (8)}

    so,

    f(x) = \frac{2}{\exp (8)} \exp(4x)
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  5. #5
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    Find the slope at of the tangent to .
    slope =

    C. A curve is perpendicular to at . What is the slope of the tangent to at the point ? slope =

    D. Give a formula for the slope at of the member of that goes through . The formula should not involve or .


    E. A curve which at each of its points is perpendicular to the member of the family that goes through that point is called an orthogonal trajectory to . Each orthogonal trajectory to satisfies the differential equation
    where is the answer to part D.
    Find a function such that is the equation of the orthogonal trajectory to that passes through the point .
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