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Math Help - Help me with these differentiation problems please!

  1. #1
    Junior Member
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    Help me with these differentiation problems please!

    a) If e^2-e^x
    Find any stationary points on the curve. (Also how would I go about drawing this curve?)

    b) The curve y=ln(x^2-3) crosses x axis at (2,0) and (-2,0). The normals at A and B meet at P. Find the coordinates of P.

    c) If y=asinnx +bcosnx show that d^2y/dx^2+n^2y=0

    thanks in advance
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Confuzzled? View Post
    a) If e^2-e^x
    Find any stationary points on the curve. (Also how would I go about drawing this curve?)

    thanks in advance
    differentiating the function with respect to x we get
    -e^x
    for stationary point it has to be zero
    which is possible only if x is a very large negative number

    graph of the function
    Are you familiar with the transformation of graph?
    If yes, here is how to graph your function

    graph e^x
    transform to -e^x
    tranform to -e^x + e^2

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  3. #3
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Confuzzled? View Post
    a
    b) The curve y=ln(x^2-3) crosses x axis at (2,0) and (-2,0). The normals at A and B meet at P. Find the coordinates of P.


    thanks in advance
    i hope A is (2,0) and B is (-2,0)

    for P, we have to find the equations of the normals at A and B
    Normal passing through A
    Slope of tangent at A=2x/(x^2-3) where x=2 comes out to be 4
    slope of normal will be -1/4
    hence equation is (y-0)/(x-2) = -1/4
    4y=2-x
    x+4y=2

    Normal passing through B
    slope of tangent at B=-4
    slope of normal at b=1/4
    hence equation is (y-0)/(x+2) = 1/4
    4y=x+2
    x-4y=-2

    the intersection point of the two normals come out to be (0,1/2) which is your P

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