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Math Help - local linearization

  1. #1
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    local linearization

    hi how do you find the local linearization of the function g(x,t) = x2cos(2t) at the point (2,P/2)

    i have no idea
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  2. #2
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    Quote Originally Posted by dexza666 View Post
    hi how do you find the local linearization of the function g(x,t) = x2cos(2t) at the point (2,P/2)

    i have no idea
    They are asking you to find the tangent plane at the point

    I guess you mean this function g(x,t)=x^2\cos(2t)

    taking some partials we get

    g_x(x,t)=2x\cos(2t) \iff g_x(2,\pi/2)=2(2)\cos(\pi)=-4

    g_t(x,t)=-2x^2\sin(2t) \iff g_t(2,\pi/2)=-2(2)^2\sin(\pi)=0

    g(2,\pi/2)=(2)^2\cos(\pi)=-4

    so finally our approximation (a,b) is

    L(x,t)=g(a,b)+g_x(a,b)(x-a)+g_t(a,b)(t-b)

    pluggin in our values gives

    L(x,t)=-4-4(x-2)=-4x+4
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